The Blues are sitting in eighth after Tuesday's defeat to Leicester, their fifth league defeat in eight games.
There remains a consensus amongst the Chelsea hierarchy that Lampard deserves a chance to get his side out of their current rut.
But the Daily Mail says that patience has an expiry date as the Blues want to secure the riches afforded to those who qualify for the Champions League.
Lampard is under no illusions about his future given the form of his team.
The Englishman is safe for now and a run of three home matches against Luton Town, Wolves andBurnley could help him turn things around.