Sherwood has been heavily linked with the job of succeeding Paul Lambert.
Lambert was sacked after Villa dropped into the bottom three with their Premier League defeat at Hull.
"This would be a real challenge for Tim but he wouldn't be fazed by it," said Allen. "He is a confident guy who believes in his own ability."
Sherwood looked poised to be appointed as Harry Redknapp's successor at QPR earlier this month but talks ended abruptly and Chris Ramsey has now been installed until the end of the season.
He was also linked with West Brom last summer, as a result of the job he did at Tottenham last season.
Sherwood stabilised Spurs following the exit of Andre Villas Boas in December, taking them above Manchester United to sixth place in the table.
He has also gained credit for the work he did with the likes of Harry Kane and Ryan Mason when he was in charge of Tottenham's development teams.
Villa dismissed Lambert after a run of 10 Premier League games without a win, during which time they collected three points and  scored two goals.
"Aston Villa is a club that is steeped in tradition," said Allen.
"Tim would certainly believe he could get them out of it. He did a tremendous job at Tottenham and people have seen that."
Tim Sherwood would not be fazed by the prospect of steering Aston Villa clear of relegation trouble, according to Tottenham academy coach Bradley Allen.