Chelsea have previously made several enquiries for Walcott and, while Liverpool and Manchester City retain their interest from last summer, Alex Ferguson has now also identified the 23-year-old England winger as a serious potential target.
Ferguson knows that Walcott's pace and ability to play out wide and through the middle would provide a new attacking option to his team.
Walcott also has an established understanding and partnership with Robin van Persie that was crucial in helping the Holland striker finish last season as the Premier League's leading goalscorer.
The attraction for Walcott of joining Manchester United is obvious. United are six points clear at the top of the Premier League and Walcott said earlier this season that he was missing Van Persie at Arsenal.
The two players remain good friends as well as former team-mates. At this stage, no formal contact or offer has been made from United to Arsenal but their interest is genuine and they are now carefully monitoring the situation.
Walcott's contract position means that he could be signed for nothing next summer or possibly at a reduced price when the January transfer window opens in three weeks' time.
Nani, who is out of favour at Manchester United and also out of contract in 2014, has emerged as a possible part of any deal. A fee to United for Nani of around £10million plus Walcott could be attractive to both clubs.
From Arsenal's perspective, they would be getting a ready-made replacement with proven Premier League experience for a price that would be reduced by the inclusion of Walcott in the deal.
Wages, however, could easily present an insurmountable obstacle in any move to bring Nani to Arsenal. Nani is currently on £80,000-a-week at United and has been pushing for an enhanced deal. Arsenal do not currently pay any player more than £100,000-a-week and are also actively pursuing other targets.
Wenger has consistently said that he will not let Walcott leave in January but has admitted to being "frustrated" by the lack of progress in negotiations and will know that it could make sense to act now rather than risk losing Walcott for nothing at the end of the season.
Walcott's ongoing refusal to sign a new contract has stemmed from two main issues. Firstly, there is a feeling that the offer of £75,000-a-week is not in line with other England internationals of comparable experience - and rather less marketability - such as James Milner, Glen Johnson, Stewart Downing, Adam Johnson and Gareth Barry.
Walcott also wants some tangible sign that he will be given opportunities to play as a central striker. He has worked hard on his finishing over the past 18 months and has scored 10 goals and created a further seven so far this season from 17 appearances.
This added composure in front of goal will ensure that United do face competing interest in Walcott. Having previously tried to sign Walcott back in 2006 when he joined Arsenal for a deal that was eventually worth £10.6m, Chelsea are expected to make their own offer next month.
Liverpool, the team Walcott supports, and Manchester City have also been interested. Walcott would prefer a club in the Champions League but will also be mindful not to risk joining a squad where he might struggle for regular first-team football.
Chelsea's London location is in their favour, as is the greater potential opportunity for Walcott to play as a central striker than at United where Van Persie, Wayne Rooney, Javier Hernandez and Danny Welbeck are all competing for places.
Arsenal would not want to sell Walcott to a domestic rival but will also want to avoid losing him for nothing later in the year when they would have no control over where he goes.
Whatever happens with Walcott, Wenger is determined to add to his attacking options next year. Thierry Henry is close to agreeing a loan move from the New York Red Bulls while bids can also be expected for Wilfried Zaha of Crystal Palace and Schalke's Klaas Jan Huntelaar.
Wenger is also keen to see more of some of his emerging midfield talent, notably Alex Oxlade-Chamberlain.
Should Walcott depart, he would be the sixth first team regular to leave Arsenal in less than two years.