Italian striker failed to score a single goal during ineffectual five-month spell with the Hammers.
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 vs Manchester City, FA Cup 2017: Where to watch live, preview, betting odds and possible XI
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.
West Ham United vs Manchester United, Premier League 2016/17: Where to watch live, preview, betting odds and possible XI
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.
However, Cheikhou Kouyate is unlikely to return from a groin injury until Wednesday's visit of Burnley.
Hammers also interested in Chelsea goalkeeper Asmir Begovic.
Arsenal are currently on the second spot in the Premier League table.
Arsenal scored five past West Ham in the league.
Dimitri Payet saw West Ham United suffer a 5-1 defeat to Arsenal in the Premier League on 3 December.
Alexis Sanchez scores a brilliant second-half hat-trick as the Gunners move up to second place.
The Gunners are short in that position with injuries to Hector Bellerin and Mathieu Debuchy.