Mourinho denied suggestions that David Luiz or Juan Mata were offered in part exchange for the 27-year-old.
And when asked if the Blues had made any other bids for players, the Portuguese said: “No – and we won’t.”
Mourinho will hold a news conference at 13:00 BST on Thursday when Chelsea land in Malaysia ahead of a pre-season tour.
The news of Chelsea’s bid came on the day United vice-chairman Ed Woodward returned early from his club’s pre-season tour.
The club insist, however, that Woodward’s return has nothing to do with the Rooney situation.
Mourinho’s comments appear to have put the onus back on United, but Old Trafford officials say they will not be bullied into selling the forward.
The Chelsea boss was speaking after his team beat Singha All-Stars 1-0 on their pre-season tour of Thailand.
Rooney’s Premier League goals
|2002-03: Six||2003-04: Nine||2004-05: 11|
|2005-06: 16||2006-07: 14||2007-08: 12|
|2008-09: 12||2009-10: 26||2010-11: 11|
|2011-12: 27||2012-13: 12||Total: 156|
He said: “We want the player. Now it’s up to Manchester United.” Asked if it is Rooney or bust, he replied: “Yes.”
Mourinho added: “I think that this situation is clear – nothing is a secret any more.
“The official bid is just about a certain amount of money and doesn’t involve players. We made the bid and now we have nothing more to say.”
United had earlier rejected Chelsea’s offer for Rooney and insisted the striker was not for sale.
Rooney has been left angered and confused by recent messages coming out of Old Trafford, most noticeably the suggestion from new manager David Moyes that Robin van Persie is his main striker.
The Scot said last week: “Overall, my thought on Wayne is that if for any reason we had an injury to Robin van Persie we are going to need him.”
Rooney has expressed his disappointment with his situation to senior figures at the club and insisted he will not accept a squad role behind the Dutchman.
United have refused to comment on the latest developments, with their players in Sydney on the second leg of their pre-season tour.
But Chelsea released a statement on Wednesday, expressing their disappointment that news of their bid had leaked out.
They also denied that any player was included in the offer, despite sources close to the talks claiming otherwise.
“Chelsea can confirm that yesterday it made a written offer to Manchester United for the transfer of Wayne Rooney,” read the 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.”
Rooney ‘problem’ may affect England – Mourinho
United insist they will not be bullied into selling Rooney, despite his disgruntlement, and are determined to deal with his future on their terms.
With Manchester City, who look set to sign Sevilla striker Alvaro Negredo this week, unwilling to follow up their historic interest, Bayern Munich and Real Madrid showing no interest and Barcelona having signed Brazil forward Neymar, Chelsea have emerged as the likeliest destination for Rooney.
Paris St-Germain have also been linked with the former Everton player, but the French champions have just signed Uruguay striker Edinson Cavani from Napoli.
In addition, Rooney is understood to be reluctant to move abroad.
He may now submit a formal transfer request to force the issue, but there is no guarantee that United will grant him a move to a Premier League rival such as Chelsea.
United are comfortable with the situation and in a stronger position than 2010, when Rooney threatened to leave only to be persuaded to stay by former manager Sir Alex Ferguson.
- Wayne Rooney Chelsea transfer: Jose Mourinho going all out to sign striker (thesun.co.uk)
- Arsenal join Chelsea in battle for Manchester United’s Wayne Rooney (guardian.co.uk)
- Chelsea Transfer Rumours: Blues Must Not Swap Juan Mata in Wayne Rooney Deal (bleacherreport.com)
- José Mourinho admits ‘It’s Wayne Rooney or bust’ for Chelsea (guardian.co.uk)
- It’s Wayne Rooney or bust for Chelsea admits Mourinho after Manchester United reject first offer (mirror.co.uk)
- Jose Mourinho: Chelsea want Wayne Rooney but won’t up transfer offer (metro.co.uk)
- Jose Mourinho warns Wayne Rooney against sacrificing England future at Manchester United (metro.co.uk)
- José Mourinho cagey over potential Chelsea move for Wayne Rooney – video (guardian.co.uk)
- Wayne Rooney Bid by Chelsea Reportedly Rejected by Manchester United (bleacherreport.com)
- Chelsea confirm Rooney bid (iol.co.za)