Despite Lampard seeming to operate with lowered expectations due to his youthful squad, Parker feels the Blues chief is under "silent pressure."
Ahead of tonight's clash, Parker told the Racing Post: "Although a lot of people are saying United are the club in trouble, I would rather be in Ole's shoes.
"I think Ole is in the better position because he's managing a massive club and Chelsea are still trying to get to that level.
"So I think if he can qualify for the Champions League, or win a trophy, he's in a much better position going forward with more potential to achieve.
"Lampard is silently under pressure because Chelsea HAVE to qualify for the Champions league, that's what their whole model is built around.
"Both sides can't afford to drop and points here and I think the pressure is on both managers. People say Chelsea are a young side but they have a lot of experience."