But Terry has urged his team-mate for club and country to focus fully on the World Cup campaign with England if he is included in Fabio Capello's final 23-man squad.
Cole has been the subject of speculation linking him a move to Tottenham and Arsenal after an up-and-down season for the midfielder, despite Chelsea winning the Barclays Premier League and FA Cup double.
On the plane? Joe Cole is expected to be in Fabio Capello's final 23-man squad
Terry is a big admirer of Cole who finished the campaign in impressive form and also did well as a second-half substitute for his country against Japan in Graz on Sunday.
But Terry also accepts that sorting out Cole's future may not be resolved before the England squad head to South Africa, and wants him to concentrate on the job in hand in the same way as Capello with his well-documented contract situation.
Terry said: 'There is the Capello contract and it's the same with the players. Joe's contract is up and so are those of a couple of others.
Alright John, I promise I'll stay!
'But his (Capello's) clear focus is to speak after the World Cup (about his contract) Hopefully, Joe will do the same. 'It's a time now to knuckle down and concentrate on us although obviously we'd love Joe to stay (at Chelsea).
'I could say it would be nice to get Joe sorted before the World Cup, but sometimes it's not as easy as that. 'We've got a massive tournament, we've got a manager - you know how he is - and he doesn't want any distractions.'
Terry has been impressed with the way Cole stepped up to the mark at club level and then latterly for England and hopes it is sufficient to convince Capello he should be part of his plans when trimming the squad down from the initial group of 30.
Chelsea captain Terry said: 'Joe has been very good. Towards the end of the season when we've needed big players, Joe Cole has been one of them at Chelsea.
'He scored a massive goal at Old Trafford and did really well. 'The manager (Capello) will make that final decision on whether to pick Joe. He's seen enough of Joe, what he's done in the last 10 days and against Japan, to know what he can do.
'With all of the lads, we all want to go and Joe's no different from anyone. He's eager to impress, eager to do extra training, eager to do anything he can to put himself on the plane.'
Should he stay? Or should he go? Cole's current deal at Chelsea has expired
Cole operated as a second striker when he first entered the action against Japan before slotting into a wide right role in the latter stages of the game. Terry said: "It was interesting to see Joe play in behind Wayne (Rooney) as well and he caused a lot of problems.
'Speaking from a defender's point of view, it's hard to know whether to go with him, stay tight or let him have the ball. 'With Ashley Cole as well, if you let him have the ball then he can cause problems.'
Terry believes the meticulous preparation by Capello will give England the best possible chance of triumphing in South Africa.
He said: 'The attention to detail the manager shows, even after the games, stressing we need to work on a few things, is great. 'He leaves no stone unturned and, when we go to South Africa, we'll be fully prepared.
'The training camp in Austria has been good, with the training at altitude, and the facilities and the training pitch were fantastic.'
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