The 36-year-old is Chelsea's record scorer with 211 goals over 13 years, but moved to City on a complex free transfer in August and memorably netted the equaliser when the teams met at the Etihad Stadium.
Lampard was cheered by the home crowd upon his return on Saturday during a 1-1 draw, and visited the dressing room afterwards, insisting he still enjoys a positive relationship with his former club.
When asked if Mourinho is bitter about his departure, Lampard told reporters: "I don't know, you would have to ask him that.
"This is football and I haven't spoken to him that much recently. I don't think there's room for bitterness and, if there is, then I'll deal with that down the line.
"Listen, I don't want to try to say there's any issue at all. I got a text from him at Christmas, I texted back. We spoke in the dressing room. We are grown men.
"We are playing for different football clubs and that's the way it is. Jose was at Chelsea, he moved on to different teams, he's come back here. Who knows what the future holds? He might move on.
"As you get older you understand that as a professional, it's your job and you move on. I'm sure we're both big enough that none of that is going to get in the way of our relationship."
Chelsea maintained their five-point lead over Premier League champions City thanks to Saturday's stalemate, but Lampard is confident the tide could turn again as the season enters the final few months.
"The result is probably better for Chelsea but it certainly leaves the title race on," he added. "Chelsea will be favourites but there's a load of points to play for. It will be on until the end."
