Southampton fullback Nathaniel Clyne has turned down a move to Manchester United.
The Sun says Clyne is not interested in following former team-mate Luke Shaw to Old Trafford.
The defender apparently has a concrete offer to join Liverpool, although Koeman and Brendan Rodgers are yet to agree a fee.
Clyne is keen for a reunion with Adam Lallana, Dejan Lovren and Rickie Lambert, with the promise of regular first-team football also a big pull.