Hayter was Cherries' top marksman for five successive seasons before he left to reunite with former boss Sean O'Driscoll at Doncaster in 2007.
Pitman, his heir to the golden boot, has netted freely for Cherries in League Two and his 21 goals including 19 in the league have spearheaded their bid for honours this season. And having plundered 114 goals in the second, third and fourth flight, Hayter is adamant Pitman could cut the mustard at a higher level with Cherries.
Hayter top scored for Cherries when they won promotion in 2003 and also hit Doncaster's winner to book their place in the Championship two years ago.
Brett is a very good finisher, said Hayter. He always takes his goals well, he's got a cool head and has all the attributes a striker needs. He isn't worried about missing chances and has confidence in his own ability.
When I worked with him at Bournemouth, you could see he had something about him. We used to do finishing practice and he had a good strike with both feet. He was a little unorthodox at times, but he would hit the target a lot and score some spectacular goals.
In my opinion, I don't think there is a massive difference between Leagues One and Two and I think he could make the step up quite easily with Bournemouth.
As a striker, you get fewer chances in the Championship because defenders are much cuter. They know when they can and can't win the ball so you have to take your chances when they come along.
Hayter, who hit 94 goals in 358 league appearances for Cherries, also believes Pitman is profiting from playing alongside his old strike partner Steve Fletcher.
It helps a lot, he said. It did with me because Fletch takes a lot of pressure off you. He talks to you and takes the physical side off your shoulders because most of the defenders at that level almost want to fight you. Fletch is so strong in the air that it creates a lot of chances for other people.
Pitman is hoping to follow in Hayter's footsteps by netting 20 league goals in a season. He registered his 19th in Cherries' 2-0 win over Accrington six days ago, although his attempts to also claim Liam Feeney's opener proved unsuccessful.
Hayter and Colin Clarke are the only two Cherries players to have hit the 20-mark in the past 38 years.
That does surprise me, replied Hayter, when informed of the statistic. I thought there would have been a few more. Hopefully, Brett can get there and help take Bournemouth up.
Theirs is the first result I look for every week and I've still got a lot of fond memories of the club.
Eddie is a good friend and we speak regularly, as I do with a few of the lads.