The 32-year-old congratulated his Chelsea teammate ahead of tonight's game against Ukraine where the midfielder is expected to make his 100th appearance for the Three Lions.
Lampard is set to join Cole and Steven Gerrard as the Three Lions' active centurions when he takes to the field in the crucial World Cup qualifier in Kiev.
Cole, who picked up his 100th cap in a friendly against Brazil earlier this year, says he will be one of the first to congratulate his club and country teammate on his latest achievement.
"I don't think he needs me to give him any advice so it'll probably be a pat on the back and just congratulate him," Cole told TheFA.com. "It's a great achievement, I think he was very nice with the comments he made about me when I did it and the same when Stevie G did it.
"I think if there's another player who does deserve it, it's him. So I'm very happy for him and hopefully we can get a good result for him as well."
Lampard has scored 29 goals in 99 appearances for England, including a record nine penalties.