A challenge would be a surprise move in the lead up to the Canning by-election in Western Australia on Saturday, seen as a crucial test of the government's performance over its two-year reign.
However a leadership change some time before year's end is widely expected.
Speculation has been mounting that Tony Abbott could face a leadership spill before the end of the year.
The Prime Minister has responded to media reports that ministers on his frontbench are pushing for Malcolm Turnbull to challenge him.
A week out from the crucial Canning by-election, Mr Abbott says he's more concerned about running the country than the latest leadership gossip.
"I'm just not going to play these Canberra insider games. I'm really not going to play Canberra insider games. We've got a terrific candidate for Canning in Andrew Hastie."
Deputy Prime Minister and Nationals Leader Warren Truss has told the ABC he believes Coalition MPs should focus on governing and working as a team.
"We have an elected leader, an elected Prime Minister, and I think it's very important that all of the team move in behind him and give him credit for his achievements, and then make sure we work constructively for the future."
Meanwhile, pre-vote polling in the seat of Canning indicates the Liberal candidate is likely to win, despite a substantial swing away from the government.
Two polls, a News Corp Galaxy poll and a Fairfax/Ipsos poll, predict a 10 per cent swing, two-party preferred, against the government on Saturday.
The swing isn't enough to unseat the Liberals in the WA seat, which is held with a 12 per cent margin, but strengthens the anti-Abbott push.
West Australian MP and frontbencher Michaelia Cash has told Sky news the result in Canning is more important than the speculation over the leadership in Canberra.
"I am not going to indulge in leadership speculation. I believe that we are a good government, and that is what I am focussing on. Just on Canning it was always going to be a tough call. Canning is one of those seats that has been held by Labor previously and it's been held by Labor previously and it's been held by the Liberal party and we currently hold it. It's a by-election, you expect a swing against the government and certainly in terms of Don Randall's personal following, he had built up a very strong personal following over a number of years. But we have an outstanding candidate in Andrew Hastie and I believe is clearly someone who has everything that the people of Canning want to serve them in the federal parliament."
Mr Turnbull has allegedly refused to publicly deny his intentions, saying any leadership chatter only fuels more speculation.
If a challenge does occur, it'll be the second move against Mr Abbott since February, when he won a party room ballot to avert a vote on the Liberal leadership.
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