Hugo Swire considered following Baroness Warsi out of the Foreign Office in protest at Government policy on Gaza, it was reported tonight.
Channel 4 News named the Minister of State as the Government figure who had discussed resignation with Baroness Warsi, who quit in dramatic fashion yesterday morning by breaking the news on Twitter while Prime Minister David Cameron was on holiday.
Mr Swire denied he was ready to resign over Government policy on Gaza. He said: "I want to be very clear - I have absolutely no intention of resigning whatsoever."
Lady Warsi's dramatic resignation - which apparently took the leadership by surprise - yesterday won praise from Lib Dems and Labour, but split opinion among Tory backbenchers.
In an interview with Channel 4 News, the peer branded the UK's policy on Gaza "mealy-mouthed" and "morally indefensible".
She said she discussed quitting in private with at least one other minister and described having a telephone conversation with a Conservative backbencher who was in tears at the devastation being shown on television.
In other developments, former international development secretary Andrew Mitchell has called for consideration to be given to imposing an arms embargo on Israel
The Conservative MP for Sutton Coldfield said he believes there is a "strong case" for trying to stop weapons getting into the conflict, while David Cameron faced calls from the Liberal Democrats to suspend arms export licences to Israel.
Deputy Prime Minister Nick Clegg said he agreed with departing Foreign Office minister Baroness Warsi that there were "serious questions" about the licences.
Fellow Lib Dem Vince Cable, whose Business Department is responsible for administering the licences, said he has been making the case for a suspension inside Government and hoped to get an agreement shortly.
Downing Street said a review of arms export licences was already under way, but stressed that such decisions should not be taken "lightly".
Speaking to BBC Radio 4's World at One, Mr Mitchell said the ceasefire in Gaza must be made permanent before talks move onto addressing the wider issue of the Middle East peace process.
On whether there is a case for an arms embargo for Israel, Mr Mitchell said: "Yes, I would have thought there is a strong case for trying to ensure that weapons getting into this conflict are minimised as much as possible.
"I think it's right an embargo should be considered."
Mr Clegg said he believed Israel has every right to defend itself from rocket attacks by Hamas but added the Israeli military operation had "overstepped the mark".
He said: "This outrageous spectacle of these three UN schools being hit by Israeli military action. That's why I believe that the export licences should now be suspended."
On suspending arms export licences to Israel, Mr Cable said: "We have been making this case inside Government but have not yet been able to get agreement for this position. I hope and expect that to change shortly."
A Number 10 spokesman said: "A cross-Government review of export licences to Israel is under way following the sustained barrage of rocket attacks from Gaza into Israel which prompted Israel to launch Operation Protective Edge. Since then no new licences have been issued for use by the Israeli military.
"Suspending export licences is not a decision we take lightly and it is right that we examine the facts fully. This is the approach being taken by the vast majority of countries.
"We welcome the current ceasefire and the withdrawal of Israeli troops from Gaza, and continue to call for a political solution to be found."
Former Foreign Office minister Sir Hugh Robertson said he did not think the Government's policy on Gaza had changed much in the last fortnight.
The Tory MP for Faversham and Mid Kent told the BBC Radio 4 Today programme: "I just don't think... shouting at them from London is going to make a difference.
"What we need to do is do the hard yards of diplomacy."