Lampard was appointed earlier this month as Maurizio Sarri’s replacement.
Mourinho, meanwhile, remains out of work after he was sacked by Manchester United last December.
Lampard was one of Mourinho’s key players at Chelsea and the pair won two Premier League titles, as well as the FA Cup during their time together at Stamford Bridge.
But despite their success, Mourinho declined the opportunity to send a message of support to Lampard, during his trip to Silverstone on Saturday.
Asked by Sky Sports if Lampard is the right appointment for Chelsea, Mourinho waved his finger and replied: “I don’t speak about football. My football? I have no football now.”
On his return to management, he added: “I am but I will wait for the right club, for the right project.
“And, in the meantime, I am doing things I like to do.
“I prefer to work, but I like other sports and this is a good opportunity to enjoy.”
