Any offer could tempt new QPR manager Harry Redknapp into a sale as it would raise the crucial funds he requires to bolster his squad when the window reopens.
At present there is only a relatively small amount of money available to Redknapp, who could also rely heavily on the loan market as he targets a striker and a central defender, in particular, in his attempt to haul QPR off the bottom of the league.
Redknapp was guarded about his plans for the window, pointing out that investment had already been made in the squad with 12 players arriving – at a cost of £14m in transfer fees and a sharp increase in QPR's wage bill – in the summer.
QPR do not have the £9m they bid for Tottenham defender Michael Dawson – who will be a target again – in August as they had to spend £3.8m on midfielder Esteban Granero because of uncertainty over whether Samba Diakite would return to the club from France, as he has subsequently done, after he suffered from depression.
Spurs would appear less likely to allow Dawson to leave in January than they were in August, with Younes Kaboul still out injured, and would resist any approach for Scott Parker, who has not played this season. Jermain Defoe is not for sale either.
Redknapp takes charge of his first match this evening, away to Sunderland, with QPR still in search of their first league victory of the season and, although the new manager reiterated yesterday that he had no intention of selling Taarabt, there was a warning that he had to work harder on the pitch.
In 2010, when he was Spurs manager, Redknapp sold Taarabt to QPR, famously calling him a "fruitcake", and the midfielder remains an erratic, if hugely talented, player. Redknapp might understandably be tempted to sell if the right offer comes in and he is given the funds to buy. It is understood that QPR would push for closer to £15m.
United have shown interest in the 23-year-old Moroccan in the past and considered an offer when QPR were promoted from the Championship.
Taarabt went on loan to QPR in 2009 before signing permanently the following year, for just £1m, becoming the key player in the club's promotion season when he was given the captaincy by then manager Neil Warnock.
"They always had great No 10s over the years. It was a good side, the team that nearly won the title on the last day of the (1975-76) season with Frank McLintock, David Webb. They had some great players and characters."
Redknapp did namecheck Dawson – "a top player" – and knows the size of the task at Loftus Road, having faced a similar one at Portsmouth.
"Portsmouth was a tough one, keeping them up when it looked like we were doomed. If I'd failed there, I probably wouldn't be alive now. This is a tough one as well.
"We keep saying we have a good team but how do you end up with four points? It's an embarrassing total for the players to have. They have to do better. They should be embarrassed.
"You can talk to players all day and those who aren't playing will blame those who are playing. Those who are playing will blame somebody else. Mark Hughes has got the sack and he's an excellent manager."
Redknapp vowed to axe any QPR player who did not pull his weight.
"We've got four points from 13 games, which is an incredibly low total. We've got to do better to give ourselves an opportunity to get out of this mess. I need people that are going to work.
"When they lose the ball, chase it. It's what you learnt when you were at school. That's what you did in the playground. I need 11 people with the ability to put effort in. And if they give that effort then we've got a chance of surviving.
"If they don't, they're not going to play to start with and I'll find another 11 who will run about and work hard." (© Daily Telegraph, London)