"I've got a year left as a player and I want to remain at a good physical level," he told bundesliga.com in an exclusive interview recently.
Scorer of one goal for the Green-Whites during an injury-hit 2016/17 season, Pizarro admitted that he accepted Bremen's decision, but also made clear that he intends to continue his inordinately successful career elsewhere.
Wherever he does so, it will be an extraordinary achievement for a man of almost 39, who began his Bundesliga journey in the last millennium. The German top flight's leading foreign-born goalscorer with 191 goals in 430 games, Pizarro credits his success at the top level to hard work on the training pitch and high fitness levels.
"I've always tried to be better prepared than anyone else," he said. "I've scored a lot of goals late on in games, when the opposition have tired. I've been able to take advantage of that because I was in good shape myself."
That commitment to personal high standards is unlikely to change as Pizarro embarks on what could be the final chapter of his storied career. His is a footballing odyssey that began in Callao, a rough-and-ready port city on the outskirts of the Peruvian capital, Lima, where Pizarro was born and has taken him to Bremen, London and Munich.
Although his father was a talented footballer and almost made a professional breakthrough, it was the siren call of the sea that turned into Pizarro Senior's profession. His son Claudio followed in similar footsteps, although on the field not the waves, making his professional bow for Deportivo Pesquero (Fisherman's Sport Club) in 1996, before joining Alianza Lima, Peru's most regal club, a year later.
Watch: Bremen's final Piza delivery
It was at Alianza that Pizarro caught Bremen's eye; despite an offer from Real Betis in Spain, Bremen "came to watch and left a good impression," and so it was to northern Germany where the striker headed in 1999.
There was an early Bundesliga connection that played a part in the decision, too: Pizarro had enjoyed the German top flight on television as a child. "Even though it was on at seven in the morning on Sundays, my dad and I always used to watch it."
The Bundesliga is a league and Bremen is a club that now hold special places in Pizarro's heart. Of his record 191 Bundesliga goals, 104 came over the course of three spells (1999-2001; 2008-2012; 2015-2017) at the Weser Stadium, although the Peruvian concedes that adapting to the rigours of the professional game in Germany was no easy task at first.
"The language didn't put me off," he said. "I came to play football and so that was my language. But the weather! I'd be out there on the pitch and it would be snowing or hailing. Sometimes I had to ask myself what I was doing there."
Adapt to Germany he did, though, to the extent that suggesting Pizarro is now half-European is well received by the striker. "I've become very organised," he says with a smile. "I'm always on time, and this is sometimes a problem with Peruvian friends. 'Tell me what time to be there and I'll be there,' I often say, because in Latin America we usually say eight when really we mean nine!"
Watch: Pizarro scores of one the Bundesliga's best goals of all time
Indeed, Pizarro adapted to life in Germany so well that he earned a move to Bayern Munich in 2001, where he played until 2007, before returning for a second stint between 2012 and 2015.
Pizarro's two spells in Bavaria were laden with success: he won six Bundesliga titles, five DFB Cups and the UEFA Champions League (among other honours).
"Bayern always win because they have such a good squad," said Pizarro. "They could play in three different leagues at the same time. Being a player in Munich brings a lot of pressure as a result, but I always coped well with that."
It was in his second spell at Bayern that Pizarro crossed paths with Pep Guardiola, the coach who left the biggest impression and who led Germany's record champions to three successive Bundesliga titles between 2013/14 and 2015/16.
Pizarro confesses that Guardiola told him that "one day the coaching bug is going to bite you," although at the moment the Peruvian has no plans to go into coaching once his playing days are up.
"Football has taken a lot out of me, and that would only get worse if I were to become a coach," said Pizarro, before admitting that if he did take up a place in the dugout one day, he "would be a maniac like Guardiola."
Watch: Pizarro's goals against Bayern and Bremen
Pizarro certainly speaks of and analyses football with the considered view of a coach and given that – bar one spell at Chelsea between 2007 and 2009 and his professional beginnings in Peru – he has spent his entire career in the Bundesliga, it is little wonder that the 38-year-old has well-thought-out views on the current state of the league.
He considers Borussia Dortmund on the same level as Bayern, but goes on to emphasise that "any of the other smaller teams can beat anyone else. You have to be in perfect physical condition to play in the Bundesliga because you're made to work very, very hard. There's a lot of running."
For a man who prides himself on his physical condition, one further year of hard work should prove little problem for the legendary Peruvian. Indeed, wherever we see Pizarro next, it is safe to say that – 191 goals later – he and the Bundesliga will forever be synonymous.