TalkSPORT reports how the 34-year-old, who is entering the final six months of his contract, will be available for transfer when the window reopens, and is free to talk to foreign clubs as early as tomorrow.
Lampard is just one goal away from becoming the second-highest goalscorer in Chelsea's history, after netting twice for the Blues in yesterday's 2-1 Premier League victory over Everton at Goodison Park.
Rafa Benitez was asked by reporters after the game whether he could shed any light on the veteran's uncertain Stamford Bridge future, but turned down the opportunity to confirm or deny whether Lampard will be leaving.
LA Galaxy have been heavily linked with a move for the England international as they seek a marquee signing in the MLS to replace the departed David Beckham. However, Lazio are also now in the hunt for Lampard's signature.
The Serie A giants are believed to have already approached the midfielder's representatives about the possibility of a move to Italy, but the club does fear it may not have the resources to match his current salary at Chelsea.