Over the last few years Fabregas has persistently been linked with a move back to the club where he began his career, but Barca's public interest in the World Cup winner has stepped up dramatically since the end of last season.
Puyol, the Arsenal captain’s international team-mate, sees no logic behind the Gunners keeping him at the club if he wants to leave.
"He is having to stay at a club where he no longer wants to be for another year," he said in The Sun.
"I wonder how intelligent it is keeping a player who doesn't want to be there.
"After seven years of great service, I thought Arsenal could have granted him his dream move."
Fabregas has made his intentions clear that he wants to return to Barcelona one day, and Puyol says he should be granted a move to the Catalans this summer because of his performances for Arsenal over his seven years at the club.
"Cesc has given everything to Arsenal to try to win a trophy but they haven't matched his expectations," added Puyol.
"I won't say he is in a prison, as we know how privileged we are as football players.
"But after how clear Cesc made it that he wanted to be in Barcelona, I thought they would have granted him that."