The Blues midfielder, who has netted 10 goals in 18 Premier League appearances this season and is just five off Bobby Tambling's all-time Chelsea record of 202, is out of contract in the summer and has not yet been approached about an extension.
|13/8||Frank Lampard is 13/8 to still be at Chelsea on the first day of next season with William Hill
And despite the England international repeatedly stating his commitment to the side, as well as the fans making their feelings clear, it is reported that the board will not offer him a new deal.
Team-mate Cole has now also come out in support of the 34-year-old, indicating that it would be a mistake to let Lampard leave.
"Of course I want him to stay," he told BBC Sport. "You don't want to lose big players like that but as I said it's not down to me or the players.
"Certainly in terms of being a player and a man and being around the squad if he goes we're going to miss him."
The left-back was speaking after the Three Lions' historic victory over Brazil at Wembley on Wednesday night, a game in which the defender won his 100th international cap.
Lampard was also the match-winner in the friendly, coming off the bench to brilliantly score Roy Hodgson's men's second goal in a 2-1 win.
Cole insisted that it was no shock to see his club-mate net his 27th England goal, hitting back at critics that say he is no longer the player he used to be.
"I see it week in week out from Frank," he added. "He's always there or thereabouts, he comes off the bench and he's still scoring goals, he's a fantastic player and good to have in the team."