The Blues legend's current contract expires in the summer, and has been linked with January moves to the USA and China as talks over an extension have reached an impasseChelsea manager Roberto Di Matteo had admitted that he does not know whether midfielder Frank Lampard will remain at the club beyond January.
The 34-year-old's current contract at Stamford Bridge expires in the summer and, with an extension yet to be agreed, he has been linked with a move to MLS side LA Galaxy and Chinese outfit Guizhou Renhe in the new year.
When questioned about the veteran's future, the Italian manager revealed he had no knowledge of the current state of negotiations over a potential new deal.
"Ultimately that's between the player and the club to agree a new arrangement," the Blues boss told reporters.
"I'm not aware how the discussions are going at the moment."
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"The players know that I would like them to stay," he added. "They are fantastic players who have always performed to a high level for us, for myself too.
"I've told them that. I hope they will stay."
Lampard has been at Chelsea since arriving from West Ham in 2001, becoming the Blues' third all-time highest goalscorer and the only midfielder to have scored over 150 Premier League goals.
The 34-year-old has made 15 appearances in all competitions this term but has struggled to hold down a starting place, and is currently sidelined with a calf strain.