Slaven Bilic has confirmed Payet has refused to play for West Ham United.
Payet signed a five-year contract with the Hammers last year.
Blues boss reportedly interested in Swansea's Fernando Llorente and West Ham's Michail Antonio.
Tony Cottee is hopeful the Belgium striker could be tempted into moving to the London Stadium.
Brendan Rodgers can develop the Frenchman better than relegation candidates, says Scott Brown.
West Ham lost the league fixture against Manchester City 3-1.
A striker is Slaven Bilic's main priority in the transfer window as he looks to arrest a poor campaign.
Algerian winger was dismissed just 15 minutes into his Premier League debut against Manchester United.
Referee has received strong criticism following a poor display during West Ham's defeat to Manchester United.
Rashford has been instrumental in United's last two wins over Middlesbrough and West Ham United.
Jose Mourinho's side are chasing a sixth consecutive win in the league.
Carrick has started in United's five league matches before missing Middlesbrough clash on New Year's Eve.
United came from behind to beat Middlesbrough 2-1 at Old Trafford on New Year's Eve.
Rooney last featured in United's 2-0 win over West Bromwich Albion on 17 December.
Marcus Rashford is finding game time hard to come by.
Drinks giant have recently been linked with a potential £200m bid for the Premier League club.
Co-owner David Sullivan admits replacement for the injured Diafra Sakho is needed.
Payet has expressed his desire to play in the Champions League.
29-year-old has described L'OM's new project under Frank McCourt and Rudi Garcia as 'interesting'.
18-year-old defender has been closely watched by the likes of Manchester United and Manchester City.
Boss suggested he may need to go into market to address shortage of options in attack.
Karius failed to deal with a saveable Dimitri Payet free kick in Liverpool's 2-2 draw with West Ham.