Reid, who was in charge of the English Premier League club between 1995 and 2002, took over the Thai national team in September on a four-year contract. However, he revealed that a clause in his contract allows him to leave if he receives an offer from an English club.
Reid told the Daily Mail he would be interested in talking to Sunderland chairman Niall Quinn about the vacancy created by Keane's decision to quit after a run of five defeats in six matches left Sunderland in the relegation zone.
"It's the place to be. The players here dream about it and I know I won't be working abroad forever. There is a clause in my contract which allows me to speak to English clubs if they show interest, so that would be up to Niall Quinn."
Despite his willingness to throw his hat into the ring, Reid is not regarded as one of the leading candidates to take over at the Stadium of Light. Sam Allardyce and Alan Curbishley both have stronger managerial track records than Reid and are available immediately having left Newcastle and West Ham respectively earlier this season.
There has also been speculation that Sunderland could approach either Gordon Strachan, the Celtic manager, or Martin Jol, the former Tottenham boss who is currently enjoying a successful spell in charge of German side Hamburg.
Quinn said at the weekend that Sunderland would not be rushed into a hasty appointment of a successor to Keane but he is due to report to the club's board on Wednesday on the progress he has made towards establishing a shortlist of candidates. The club have reportedly received more than 50 applications for the vacancy.