Mourinho has faced criticism for his style this season, with United falling eight points behind runaway leaders and rivals Manchester City.
United (23 points) are back in the chasing pack, along with Tottenham (23), Chelsea (22), Liverpool (19) and Arsenal (19).
But Lampard – who won three Premier League titles at Chelsea, including two under Mourinho – said it would come down to the quality of players at his former manager's disposal if United were unable to claim the crown.
"Mourinho is a manager that likes to win and he has a way of winning. It's different to Pep Guardiola, different to Antonio Conte and that's his way," he told Omnisport, giving thanks to Chelsea FC club partners Yokohama Tyres.
"If Manchester United don't win the Premier League, for me it's the quality of the players.
"Manchester City have a very strong squad this year, Chelsea still have a very strong squad and I think particularly the first XI, if everybody's fit, Chelsea are very strong.
"When I look at Manchester United, they're there around that area, but maybe the other teams can be stronger.
"I certainly don't think it'll be the manager, and I actually do think that Manchester United will be competitive towards the end of the season, so we'll see."
United have won just one of their past four league matches, having drawn with Liverpool (0-0) and lost to Chelsea (1-0).