According to Spanish outlet Cope, The Spaniard could be frozen out of the Blues squad for the remainder of the season after Willy Caballero featured in the 2-2 draw at Leicester.
The 25-year-old has been criticised by supporters and pundits during a campaign in which he has conceded 43 goals and kept eight clean sheets.
And Lampard is expected to look for long-term replacements while Caballero deputises for the Spain international.
After his first league start of this term, Caballero told the Chelsea club website: ‘The day before the game we trained and I was with the starting XI.
‘It was a difficult moment for Kepa, for the team, and we respect very well each other. Also for the boss it was really tough.
‘He told me just to be confident. It was a difficult decision from him, but I just had to take it and enjoy. It was very honest, the message from him.
‘As a goalkeeper I have to switch on very quickly and be ready for this opportunity, because I’ve been working and training really hard for it.
‘I feel great because I played and we got one point in a difficult stadium against a difficult team.
‘We’ll see what they want to do and I’ll just keep showing that I can play and be in the starting XI for the next game.
‘But no one is sure that they will play the next game. The message from the boss is to keep working hard in training.
‘I had the opportunity to play and to try to enjoy it. I just have to do my job, be ready for the next game.’