It would mean Bayern, should they not want to offer an extended contract to a player now in his 30s, would have to sell Martinez this summer if they wish to receive a transfer fee.
The player himself is not pushing for an exit despite playing a reduced role this campaign as Bayern claimed an unprecedented eighth successive German league title.
It is understood that Martinez is enjoying working with Bayern head coach Hansi Flick, and if fellow Spanish midfielder Thiago Alcantara leaves the club this summer, a first-team berth could open up for him again.
It has been claimed that Thiago may be seeking a new challenge away from Bavaria, and has been heavily linked with a move to Premier League champions Liverpool.
Martinez made just six Bundesliga starts in the 2019-20 campaign as Flick’s side won the title by a sizeable 13-point margin.
He has suffered with injuries in the past year, most recently missing Bayern’s DFB-Pokal final victory over Bayer Leverkusen because of a gastrointestinal infection.
In spite of a reduced role in the last year, Martinez has enjoyed a hugely successful eight-year spell with Munich since joining from Athletic Club in 2012 for €40 million (£35m/$45m), winning 19 major trophies.
Martinez spoke to Marca about his future in June, claiming he was in no rush to leave Bayern: “What I have experienced here was great. We have to wait because there is a lot of uncertainty.
“We do not know whether there will be a transfer market or whether the Champions League will be played [due to the coronavirus pandemic].”
He did, however, admit to considering his options and said he would be open to a return to his old club: “I am open to everything that fulfils me personally and physically. I could live and play in the USA, in Australia, or return to Spain.
“I had six unbelievable years in Bilbao. Of course it is an option.”