Nasri's contract runs out at the end of next season and talks over a new deal have stalled, with the midfielder reportedly unhappy with the salary on offer.
He struck fear into the heart of Gunners fans at the weekend by refusing to rule out a move to Manchester United - and Walcott concedes Nasri could be headed to one of Arsenal's rivals.
"I don't like getting involved in people's careers," Walcott told Sky Sports News. "We need to keep hold of our best players - but it's up to Samir, it's his decision. He had a great season, he showed people what he can do. He's a very important player to Arsenal and we'll see what happens in the summer."
Meanwhile, Walcott has backed manager Arsene Wenger's declaration that he will be more active than usual in the summer this year. Wenger is believed to be targeting defensive reinforcements - ideally ones with experience of Premier League football - as he looks for Arsenal's first trophy since the 2005 FA Cup.
"Yeah [I'm expecting players to be signed], the manager's said so," Walcott said. "Hopefully we can keep hold of our best players, as we need to be winning something next season without a doubt. It's been so long and the fans have waited so long. And players don't like seeing every season go without winning anything."
Walcott hopes some summer signings can help give Arsenal a ''cutting edge'' next season.
''It will be interesting to see who comes and goes in the summer, the boss has said he is going to spend,'' Walcott told BBC Sport. ''We have got a great squad and play the best football, it is just a cutting edge which we need.
''It is disappointing for us players because we want to give the fans something to cheer about and we want to be in the history books. It was not meant to be this season, but we have shown great potential, with Jack Wilshere coming through, Aaron Ramsey is coming back to form as well, which was great to see, so I think it will look quite good for us next season.
''It has got to be because there is a lot of competition with Manchester City and Liverpool coming into the frame now, so it is going to be a very interesting Premier League.''