Bassett, the former Wimbledon manager who was replaced by Howard Kendall at Sheffield United, was one of those linked with the Republic of Ireland vacancy. Mike Walker, the former Everton and Norwich City manager, is also thought to be among the candidates.
The Millwall chairman, Peter Mead, warned that the man who follows McCarthy into the Lions' Den faces a demanding challenge. "It is a tough act for anybody to follow with a line-up of previous Millwall managers including George Graham, John Docherty, Bruce Rioch and, of course, Mick," he said. "So, although the decision needs to be made quickly, we must carry on that tradition.
"I still believe that with a fresh impetus we are in with a good chance of being involved in the final shake up at the end of the First Division season. Everything we do will be aimed towards that."
Mead considered McCarthy's appointment by the Irish as "a great compliment" to Millwall, adding: "On a personal note I am sad that I am losing a manager whom I admire enormously and a friend. He brings to his new job great qualities, particularly in the area of decency and integrity. As far as a new appointment is concerned, I have my own ideas and I am actively pursuing them."
Mead may be left with two vacancies. Ian Evans, McCarthy's assistant, is being tipped to follow him into the Republic set-up as the manager of the Under-21 side.
The Football Association of Ireland is trying to negotiate a parting settlement with Maurice Setters, who did that job under Jack Charlton.
n There was good news for another south London club. Nigel Martyn, the 29-year-old former England goalkeeper, committed himself to Crystal Palace by signing a new three-year contract.Reuse content