The former Hull and Derby boss, a defender at Pools in the early 80s, met chairman Ken Hodcroft for a first round of talks.
Brown was the runaway favourite with the bookmakers before betting was suspended on Wednesday evening.
But the process of appointing Neale Cooper’s replacement still has some way to go. Micky Barron will remain in charge for tomorrow’s game at Yeovil.
Craig Short, the ex-Notts County and Ferencvaros boss, is also on the list, along with Colin Cooper, the Middlesbrough academy coach and both also watched Wednesday’s game.
With back to back home games to come, Coventry a week tomorrow followed by Oldham three days later, the new manager will be appointed early next week.
Barron and his players set off this morning for the trip to the south west. They’ve not won in 15 games, but the stand-in boss was satisfied with the performance against Tranmere – while disappointed they couldn’t maintain the level displayed for the first hour.
Pools were awful in being thumped out of the FA Cup last weekend and Barron said: “I thought we got the reaction I wanted. The players got the crowd going and they did owe them something.
“You cannot say the application wasn’t there in this game, unlike last weekend.
It’s a step forward and that has to be the basics expected of them.
“We wrote a list of words up before the game which they have to adhere to.
“Brave was one of them and they were brave in character.
It’s a shame they didn’t do as well second-half, maybe they had a bit of worry or not wanting to get on the ball and give it away.
“The momentum then changed to get Tranmere on top.’’ Pools started the half with their best chance of the game, but Jon Franks saw his effort saved.
Franks, signed from Middlesbrough in the summer, was impressive and Barron admitted: “It would have been nice to get in front, but you don’t want to dwell on things.
“Jonny hit the target and the keeper saved it, it could have been something to build on.
“If it was one of their players, it might have gone in.
It’s a mistake, he has tried to score.
“He had a good game, I’ve spoke a lot to him. He was negative at the start, but I wanted him to get on the ball and be positive and one run he had gave him a lift and started being a threat. It’s the standard we want.’’