Sir David Murray says it would be in the best interests for all that debt-ridden Rangers are sold sooner rather than later.
Gers are currently under strict financial control despite retaining their SPL title and securing a place in next season's UEFA Champions League.
Rangers have been up for sale all season and Murray has confirmed any potential buyer would be securing a debt-free club as the proceeds from a takeover would be used to pay off their estimated £31million debts.
Murray has recently held talks with property tycoon Andrew Ellis over a possible takeover, while there has also been reported interest from other parties.
"The sooner a deal is concluded the best it will be for all," he told the Scotsman.
"A buyer would pay a figure to buy a debt-free club. Rangers are in a much-improved position."
The club confirmed this week they are being investigated by HM Revenue and Customs about offshore payments made to players.
Gers could be liable for millions should the taxman win, although Murray believes the club have a strong case, adding: "We have a strong case according to our lawyers and will robustly defend it."
No slacking off
Meanwhile, striker Kenny Miller insists Rangers will not be slacking off between now and the summer after clinching the title at Hibs last weekend.
Walter Smith's side tackle Dundee United this weekend before another Old Firm clash against Celtic midweek followed by a home fixture against Motherwell.
"It won't take a lot of motivation next Tuesday because it's an Old Firm game so we will be up for that," said Miller.
"The lads are already looking forward to it. They are huge games no matter what the situation is.
"An Old Firm game is an Old Firm game so you've got to battle and you've got to win the games.
"We've been fortunate this year that we've got two wins and a draw and it would be nice for us to get another win and finish off the season in a good way.
"We want to go there and get a good result and then finish with a good result in front of our own fans on the last day of the season on the day we are going to get the cup."