Wheater, whose departure has edged closer, also attracted a new enquiry from another club over the weekend.
The 23-year-old was at Rockliffe Park for training yesterday after impressing in Saturday's win at Bristol City.
Bolton had been looking to do a deal for around £2.5m for the centre-half and had indicated a reluctance to meet Middlesbrough's demands of around £3m rising to £4m.
And when they realised the Teessiders were determined to land their asking price for a player who will be free to leave for free in the summer, Bolton cooled on negotiations.
However, Trotters boss Owen Coyle wants the defender in his squad this month and it is believed fresh discussions have taken place.
Boro manager Tony Mowbray would prefer to have Wheater for the long term and there have been discussions over a new contract.
But with the Redcar-born graduate of the club's Academy showing an intention to play in the Premier League, selling this month remains Boro's best option.
There is plenty of interest in the player, with the likes of Wolves, Everton, Newcastle and Stoke all keen.
But only Bolton are known to have tried to reach an agreement over a fee.
Mowbray, whose side climbed three points clear of the Championship's relegation zone by winning at Ashton Gate, would prefer for the situation to be sorted well before the closure of the transfer window on January 31.
Andrew Davies, who has been training with the club for the last six weeks, looks likely to arrive on loan from Stoke City if Wheater departs.
They are also looking at lower league replacements.
The Boro boss has already been hit by the significant news that midfielder Kevin Thomson faces a struggle to play again this season.
It has emerged Thomson has been playing with a hairline leg fracture for a number of weeks before he was forced off at Elland Road on New Year's Day feeling further pain.
Initial tests failed to show up the severity of the injury, although further scans last week revealed that he was facing a lengthy spell on the sidelines.
Thomson's injury has reduced the number of options Mowbray has in the middle of midfield, although he has been credited with interest in Kelvin Ethhu, who is available on a free transfer from Manchester City.
Source: Northern Echo
Source: Northern Echo