The former Blues and United goalkeeper expects the England striker to leave Old Trafford this summer but says the club should not sell to one of their biggest rivals
The Red Devils rejected a second bid from Chelsea for the striker on Sunday, understood to be worth £25 million plus add-ons to take the deal to just under £30m.
Bosnich says the Premier League champions were right to reject the offer and should avoid selling the unsettled forward to the Blues if they can.
"Manchester United shouldn’t sell Wayne Rooney to Chelsea, who are one of their biggest rivals. From the club’s perspective that would be suicide," he told talkSPORT.
The former Australian international believes manager David Moyes should instead sanction a move to Arsenal as the north London side pose less of a direct threat.
He continued: "Rooney can hurt them if he goes to Chelsea. If there was a choice between Arsenal and Chelsea, the lesser of two evils would be Arsenal.
"It’s very difficult to sell one of your best players to a club that can hurt you.
"Manchester United have come out very clearly and said they don’t want to sell Wayne Rooney. But if a player is not happy at a club then you are best off selling him."
Despite Manchester United signalling their intention of holding on to the England striker, Bosnich sees a summer move to be inevitable.
"It’s quite obvious he’s not happy. He was unhappy last season at not being a starter and when he was dropped for the Champions League tie against Real Madrid there were going to be problems," he added.
"David Moyes has come in [as manager], they have a history together, both good and bad, and he was willing to let bygones be bygones, but I think Rooney wants a new challenge."