Optimism that Amanda Staveley will persuade Mike Ashley to sell Newcastle United to her Dubai-based PCP Capital Partners Middle Eastern investment fund rose on Wednesday when the Yorkshire-born financier increased her offer for the club to around £300m.

It is believed an agreement between Ashley and Staveley, who met for the first time at an Indian restuarant in London last week, is now close with a takeover on course for completion by late January or early February.

While that would come too late for the January transfer window there are suggestions Ashley could offer Rafael Benítez, Newcastle’s manager, around £30m to spend on the players needed to avert a relegation skirmish. Staveley would refund the money once contracts are signed.

If, and when, Ashley accepts her offer it would signal the starting of a four-week period of due diligence after which the fine details of the deal would be negotiated. Staveley and her investors would be subjected to the Premier League’s fit and proper persons test. That vetting process can also take around four weeks but things could be slowed by the Christmas and new year holidays. Staveley intends to assume a hands-on role at St James’ Park and become the public face of the club.

Ashley bought Newcastle a decade ago and has invested around £260m in the club. He had hoped to sell for nearer £400m and turned down Staveley’s opening £250m offer. The Sports Direct owner has not yet accepted the improved bid but it is understood he is minded to do so.

Once a price is agreed both parties will enter a period of “exclusivity” in which any other potential buyers are excluded. Ashley had seemed reluctant to take such a step but Newcastle’s poor form appears to have accelerated matters. Before Wednesday night’s game against Everton, Benítez’s team had taken only one point from their previous seven games.

If an awareness that relegation would prompt a drastic depreciation in Newcastle’s value looks to be hastening the owner’s desire to reach an agreement, certain compromises are still to be made. Even so, it is thought Staveley would be agreeable to retaining the Sports Direct signage at St James’ Park – effectively free advertising for Ashley’s company – for a limited period.

The identity of Staveley’s backers remains opaque but the 44-year-old is believed to have secured funding from the Middle East – quite possibly Saudi Arabia – and China. A skilled negotiator possessing peerless contacts in the Gulf, she masterminded Sheikh Mansour’s 2009 takeover of Manchester City.

Staveley’s latest ambition is to try to put Newcastle in a position where Benítez’s team can compete with City in the Premier League and the Champions League.