United have been repeatedly linked with the decorated Mourinho, who was sacked by the English champions in December following their dire run of domestic form.
Red Devils boss Louis van Gaal has been under pressure for much of the campaign, with the side currently sixth in the Premier League standings following a 1-0 defeat to West Brom on Sunday.
"If I’m in charge at United and I see Pep Guardiola going to Manchester City, Jose would be top of my list," Lampard is quoted as saying by The Mirror.
"Jose will get the best out of the players there. He will recruit top players.
"They are not happy with where they are at. It’s a good option for both United and Jose. It's a good fit."