The former Chelsea duo could go head to head on Tuesday, when City host Roma in the UEFA Champions League.
Lampard, on loan at Manchester City, has scored four goals in his past three matches " including an equaliser against Chelsea.
Cole talked up Lampard and said he was looking forward to catching up with the 36-year-old midfielder.
"I think everyone knows what Lampard brings to any team," he told a news conference.
"And it's another great experienced player for City and of course he brings goals and so far from what I've seen he's scored goals.
"He scored against Chelsea. They probably didn't like that but he had to do a job and that's what he's paid to do.
"Of course it was probably a little bit disappointing for him to score against Chelsea but that's what his game is, to score goals and again it will be really nice to see him."
Cole, who like Lampard left Chelsea at the end of last season, hopes to see his form improve for the Serie A giants.
"I'm not playing that well, I won't get carried away, I know I could do better, I maybe just need a little bit more games," he said.
"But like I keep saying I'm enjoying my football here and hopefully I can keep playing and emulate what I did at Chelsea and of course at Arsenal."