The 36-year-old former Italy defender, who began his career with Lazio, helped Milan win two Champions League finals and two Serie A titles.
"When I finish the season I think about the following one, and I think that with the rhythm of the season, what with the Champions League and everything else, I won't be able to play all the time," Nesta told reporters at Milan's training ground.
"And seeing as I can't just sit on the bench and wait my turn... if I don't feel like an important part of the team then I would prefer to stay at home.
"Out of respect for the club and myself I would prefer to go and experience something different where I can still enjoy myself, do something good."
There has been speculation that Nesta, who was in the Italian World Cup-winning squad in 2006, will move to the United States to play in the MLS, with the New York Red Bulls looking the most likely destination.
"I don't know where I'm going to go, I haven't signed with anyone, but I know that I'm leaving a great club where I had a great experience," he said.
"Going there (the USA) wouldn't be bad, I would gladly go there, it would be a great experience."
This season has been something of a disappointment for Milan, who lost their title to Juventus, and only reached the quarter-finals of the Champions League, where they were knocked out by Barcelona.
"I'm leaving Milan disappointed because we hoped to win a league title that was within our grasp. There is disappointment, while no-one knows about the future because there's a good group of players that will leave. If you spend to renew the squad you'll stay at the top, but I don't know what the club wants to do."
Nesta leaves behind a whole host of happy memories, including beating Juventus on penalties in the 2003 Champions League final at Old Trafford which Nesta described as his "favourite victory".
"I'll miss everyone," he said. "I want to thank everyone that works at Milanello (Milan's training ground). And naturally I will miss my old team mates like (Massimo) Ambrosini, (Gennaro) Gattuso, (Clarence) Seedorf, (Paolo) Maldini, (Alessandro) Costacurta and Andrea (Pirlo). I came to Milan as a Roman and I felt better here than at home."