Craig Conway, Prince Buaben, Morgaro Gomis and David Robertson are all set to make their final appearances for the club before heading to pastures new when their contracts expire.
Houston, who guided the team to the cup win over Ross County last season, wants fans to give the quartet of heroes a send-off to remember, saying: "I would love the fans to turn out in numbers for the players who are leaving."
He added: "I am going to play as many of them as I can. They will go down in the history books because Dundee United don't win the Scottish Cup that often.
"The team from 1994 are still celebrated these days and I think in 20 years time the current crop of lads will be looked upon in the same way.
"They will be invited back to Tannadice and welcomed by everyone.
"The boys have decided to move on, change their careers and maybe make a bit more money.
"The fans have been great to them, though, and Sunday is a wonderful opportunity to show their appreciation one last time.
"Although there is nothing to play for the lads will want to end the season on a high and I'm sure Hearts will as well."
Source: PA
Source: PA