The Ghanian, released by Carlisle United earlier this summer, yesterday made his third appearance as a trialist for the Tynecastle club and opened the scoring in a 3-0 win over East Fife. The 26-year-old is expected to formalise his stay by signing a one-year contract early this week.
Erstwhile Crystal Palace striker Osman Sow also featured as a trialist in Methil and the Swede did his chances of earning a contract no harm after scoring Hearts' third goal, following an earlier effort from Gary Oliver.
"I thought Prince did well again," said Neilson. "We're speaking to his agent and he has a year on the table just now. Hopefully we can get something done by Monday or Tuesday."
Neilson remained coy on the prospect of adding Sow to his squad, although the coach was no doubt impressed by Swede's work in setting up the opening goal.
Hearts were able to look quite relaxed when they went ahead through Buaben, who pounced after Billy King hit a post with his initial shot. Oliver scored with a header after 25 minutes and Sow then prodded in the third after robbing keeper Allan Fleming.
Hibernian have, meanwhile, appointed ex-Hearts goalkeeper Alan Combe as a coach. The 40-year-old was a casualty of Ann Budge's Tynecastle takeover in May and is set to cross Edinburgh to join Alan Stubbs' backroom staff.
The Scotland B internationalist could also be registered as a player at Easter Road for next season. "If he is willing then we would be foolish not to register him," said Stubbs, who also expects to confirm Andy Holden's arrival as coach this week.
He was in the dugout yesterday as Hibs defeated Berwick Rangers 4-0.
Elsewhere, Dundee United finished off their tour of Ireland with a 4-0 win over Bohemians.
Inverness beat Elgin 2-1 at the Borough Briggs, but St Johnstone had to rely on a David Wotherspoon equaliser saving them from defeat against Raith Rovers.