The 36-year-old ended a 13-year stay with the Stamford Bridge outfit in July after agreeing to join new MLS outfit New York City on a free transfer, but is now set to join the Premier League champions until January.
The likes of former Chelsea manager Carlo Ancelotti and Arsenal boss Arsene Wenger have queried the move, but Mourinho insists Lampard is free to do whatever he wants following the expiry of his Chelsea contract.
"He is a free agent, he can choose his club so there's no problem at all," he told reporters.
"When he comes to Stamford Bridge he is welcome."
Lampard is expected be registered for both City's Premier League and Champions League squads as he looks to maintain fitness ahead of the start of the MLS season in March, 2015.
The England international scored 211 goals for Chelsea in 649 matches and is believed to be keen to avoid a potential match-up with his former employers. City face Chelsea at the Etihad Stadium on September 21.