Gallas said this ahead of Chelsea’s Premier League tie with Fulham on Saturday evening.
Lampard’s men have slipped to ninth position on the log and are 10 points behind league leaders, Manchester United.
“I think Lampard’s position is in danger,” Gallas told Play OJO.
“He is not in a good position right now as they are not in the top three at the moment.
“They spent a lot of money, so the board wants to see Chelsea winning the Premier League.
“I thought this season that they had a great chance to win it, but at the moment I am sure the board are not happy with the results which is why I am sure Frank is in a dangerous position.
“He needs to try and finish in the top three or win the Premier League.”