Dodds took charge of Sunderland on a caretaker basis after Tony Mowbray was sacked earlier this month.
He has won both his games, against West Brom and Leeds, respectively and is likely to be in charge for Sunderland’s visit to Bristol City this weekend.
Bennett is certain that Dodds at least wants to remain in charge until the end of the season at the Stadium of Light.
The Sunderland legend feels that there should be no reason why the caretaker boss should be let go for a new permanent boss if Dodds keeps winning games.
He also indicated that the arrival of a new manager could disrupt Sunderland’s momentum at this stage of the season.
Bennett said on the BBC’s Total Sunderland podcast: “Of course, he does [want the job].
“It’s a tremendous job to have but what he has got to do is to continue winning games.
“If he does that then I can’t see why he shouldn’t get the job until the end of the season.
“How long do you give him? Another two or three games or the festive period?
“You bring in a new manager but does he change things? And if he changes things, does that benefit the team? Do we lose our focus?”
Sunderland are looking at a host of options to become their next manager, but Dodds’ performance has likely given them food for thought.