The 31-year-old is free to leave next month having agreed only a short-term extension to cover the end of the campaign.
He is in a race to be recover from injury in time for Saturday's FA Cup Final against Arsenal (Stream live on ESPN+, 12.30 p.m. ET) before Chelsea face Bayern Munich in the Champions League, round of 16 second leg clash on Aug. 8.
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Talks over a longer-term deal have been deadlocked for months with Chelsea only willing to offer Willian a two-year contract while the winger has insisted he wants a minimum of three years.
However, Lampard has been adamant that he wants Willian to stay at the club and is believed to have given him assurances he will play a key role next season despite the £37 million arrival of Hakim Ziyech from Ajax.
It is unclear whether Chelsea will finally increase the length of their contract offer or Willian will relent in return for an increased salary and bonus package but negotiations remain ongoing and the two parties are expected to discuss the situation again in the coming days.
Lampard is concerned about a lack of squad depth and after Chelsea qualified for the Champions League on Sunday with a 2-0 home win over Wolves in the final round of Premier League matches.
He is keen to retain Willian given the wealth of experience he has accumulated since joining the club in 2013.
However, the player's preference has always been to stay in west London and sources at the club have expressed hope that a breakthrough can be reached soon.