Jose Mourinho insisted the future of Wayne Rooney is a decision for Manchester United as the tussle for the striker's services began in earnest.
Mourinho was low-key when commenting on the offer in Bangkok on Wednesday, despite United provoking the Blues' ire.
Chelsea confirmed they want to buy Rooney, who is in dispute with United over comments made by manager David Moyes when he spoke to journalists in Bangkok last week.
Speaking in Bangkok following the first match of his second spell in charge - a 1-0 win over Singha All-Stars - Mourinho declined the opportunity to fuel the argument.
"I think that this situation is clear - nothing is a secret anymore," he said.
"The official bid is just about a certain amount of money and doesn't involve players.
"We want the player. We made the bid and now we have nothing more to say. Now it's up to Manchester United."
Asked if Chelsea had made any other bids, Mourinho said: "No, and we won't."
Asked whether it is now "Rooney or bust", Mourinho said: "yes."
The Londoners are certain United were responsible for the suggestion of a part-exchange, which they insist was not true.
"Chelsea Football Club can today confirm that yesterday it made a written offer to Manchester United for the transfer of Wayne Rooney," said Chelsea in a statement.
"Although the terms of that offer are confidential, for the avoidance of doubt and contrary to what is apparently being briefed to the press in Sydney, the proposed purchase does not include the transfer or loan of any players from Chelsea to Manchester United."
Asked specifically about any proposal to swap a player or players for Rooney, Mourinho said: "For me, no more comments. I have to respect Man United and my colleague David (Moyes, the United manager), to respect even my players from Chelsea.
"The bid is there. The club knows we want the player. The player has to know we made a bid for him.
"Now it's up to them and we respect their decision. I work with my players now, as I've done from day one.
"I trust my players, I'm happy with them and that's what I have to do now.
"We did what we had to do in a proper way, in an ethical way, and we're very happy with our behaviour. It was clean.
"Now I keep doing what I'm doing, working with my players, trying to improve my players, and we'll see what happens. Now he's with Man United, not with us."