Chairman Steve Gibson is currently assessing his options after deciding to dispense with the services of Pallister's former team-mate Tony Mowbray last month.
Gibson, who has placed Mowbray's number two Mark Venus in interim charge, has been inundated with expressions of interest.
But whoever finally gets the nod, Pallister hopes it is someone who can identify with the club and the town.
He said: "Some of them (the men linked with the job) are very interesting and I am sure would prick the imagination of a lot of Middlesbrough fans.
"Whether they go for the big-name signing or somebody who already knows the players is something they have got to get right at boardroom level.
"Hopefully they will do and hopefully we will get somebody that has a real feel for the area as well and embraces all that Middlesbrough is about and can take the club forward.
"The fans need to lift the team and the team needs to lift the fans, so it's a two-way thing. Somewhere down the line we have got to try to merge all that together and get that support back in the stadium and give them something to cheer."
Pallister, now 48, began and ended his playing career at Boro and has seen the club's fortunes rise and fall over the years.
The Teessiders are currently spending their fifth successive season in the Sky Bet Championship and he is desperate to see them back at the highest level.
He said: "The club is a different club from what it was 10 years ago, going back to when I left and Steve McClaren came in.
"It's had to cut its cloth accordingly - we don't see the big-money signings anymore, and that's by the very nature of being back in the Championship and having lost the parachute payments.
"We are a club that has been a yo-yo club for many a year, but it would be nice to bounce back one more time and see if we can stay there a bit longer."
Pallister admitted his disappointment at Mowbray's demise but backed a man who was a central figure in the club's fightback from the brink of liquidation in 1986 to bounce back.
He said: "I have seen close friends like that and team-mates lose their jobs and it's sad because you want to see these guys go on and have successful managerial careers.
"But I am sure he will bounce back. I am sure there are a lot of people sad on Teesside because he was hero here, and rightly so the way he played in that red shirt, bringing the club through '86 and all that. He is going to live long in the memory here."
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