The Hammers are willing to offer £9 million for the England international.
But Le Tissier told talkSPORT: "I'd be surprised.
"£9 million is a lot of money for someone of Rickie's age and the number of seasons he's got left in the Premier League, not for his ability though.
"West Ham are in a position where they need to find somebody who can score some goals so they may well try again to sign him, having failed in the summer.
"From what I know though and what I hear, Rickie is pretty happy at Southampton so I'd be surprised if he left."