Chief executive Peter Kenyon claims it is '50-50' whether the pursuit of Andriy Shevchenko will result in the player joining Chelsea.
The Ukraine striker has been linked with the Blues ever since the acquisition
of the club by Russian owner Roman Abramovich.
A move to Stamford Bridge appeared more likely after the striker announced in the week he wanted to leave present club AC Milan, although the club are determined to hold on to him.
While admitting the clubs have spoken about the player, Kenyon insists there is a long way to go before any negotiations could be concluded.
Kenyon, who was speaking on the team's open-top bus tour parading the Premiership trophy, said: 'I think Shevchenko is the type of player we would like. We have shown our interest in him the last two seasons and had dialogue with Milan.
'At the end of the day to improve what we have got, it has to be a great player and Shevchenko certainly comes into that class.
'You stand a chance but you don't put it any more than that. There is a long way to go in the summer.
'It has got to be 50-50 but I wouldn't say any more than that.'
Manager Jose Mourinho also played down the possibility of Shevchenko joining the Blues.
'I think the natural thing is that you have a big striker to join us and to make this group stronger,' said Mourinho.
'I cannot say it is Shevchenko - Shevchenko is a player that belongs to Milan and Milan have a three or four-year contract with him and they can say the same thing we are saying in relation to (William) Gallas - no offers and no way of leaving because this is the power the clubs can have when they have a contract with the players.
'I'm optimistic first of all of keeping every player (that is) important for us and after that I'm optimistic to go after players of big quality - Shevchenko and another one.'
The Blues boss wants to make three signings this summer - with a trio of his current squad making way - and Michael Ballack is set to be the first arrival with the Germany midfielder set to be unveiled at Stamford Bridge tomorrow.
Mourinho said: 'I'm very happy with the conversation I've had with him and the reasons why he decided to come here.
'He believes in us, he believes in Chelsea, he believes he'll have the chance, he believes in the Champions League, he believes in three or four years success for him in a crucial part of his career.
'He has had a lot of other chances as you can imagine. He decides on Chelsea and we are very happy and I think also English football should be happy to have such a player in the Premiership.'
Kenyon confirmed the club are looking to tie the deal up imminently, adding: 'We are looking to conclude that on Monday and that looks good. As normal we are not in the market for lots.
'You are up against all the major clubs in Europe [to sign him] so you are in strong competition but I think what we offered him at Chelsea in terms of our sporting ambitions swung it.'
However, Kenyon played down reports of a move for Corinthians forward Carlos Tevez, adding: 'We have looked at him and he is a good player and does a good job but all the reports of him being linked with us are not right.
'I would be surprised to see him in a Chelsea shirt next season.'
William Gallas has said he wants to leave Stamford Bridge despite being offered a four-year contract.
The France international has been with Chelsea since his move in 2001 from Marseilles but has been frequently linked with a move to the San Siro to join Milan.
The 28-year-old did not go on Chelsea's parade and Kenyon said: 'He is under contract for another 12 months. We have made it clear we want to keep him but if he wants to further his career he can do it at the end of his contract.
'He still has 12 months to go on his contract.'