While captain Fabregas has been strongly linked with a move back to boyhood club Barcelona, Nasri has reportedly been targeted by North West rivals Manchester United and Manchester City.
Despite Gunners boss Arsene Wenger’s claims that he wants to keep hold of the midfielders, McLintock thinks that they should be let go.
“I’d let Fabregas go. We will miss him, he’s a magnificent player, but he’s had six or seven great years with us and now he’s desperate to go to Barcelona,” McLintock told talkSPORT.
“So wish him all the best and let him go. And I’d do the same with Nasri.
“If the fella’s adamant he wants to leave I wouldn’t want someone in my club who would spread a bad feeling in the dressing room. Sell them and get some star players in, not free transfers.”
The London club, who were booed by home fans during the Emirates Cup this summer, signed Lille frontman Gervinho last month. However, McLintock is adamant the Gunners need to strengthen their squad.
“It would be nice if Arsenal gave something back to the fans by buying three or four top class players,” he added. “We are looking very vulnerable and we’re the only team that doesn’t seem to buy anyone.
“It doesn’t look good for Arsenal. The vast majority of supporters would like to see two or three new players. It’s very frustrating for the supporters, and I’m one of them. We’re all very concerned. Most of us feel if we don’t strengthen quite a bit we’ll struggle to get into the top four.”
Arsenal kick off their Premier League campaign with an away trip to Newcastle on August 13.