Celtic will be looking to finish the season “as strongly as possible” regardless of when they clinch the Premiership title.
The champions-elect could all but win the league if they beat Hearts at Celtic Park on Saturday.
Although it won’t be mathematically finished, Celtic’s superior goal-difference means they could realistically claim their 52nd league title, and 16th since the turn of the millennium 22 years ago, with one more win from their last three games.
But Ange Postecoglou is taking nothing for granted and will demand the players live up to their own high standards in their remaining three games.
Speaking on Friday, after being named Manager of the Month for April, he said: “From my perspective I want to finish as strongly as possible and play as well as we can in the last three games, starting against Hearts.
“If that coincided with us getting the prize then great, but ultimately we are still in a position where we need to play well in the last three games and get the results we need.
Celtic will go nine points and at least 20 goals clear of Rangers if they beat Hearts, but Postecoglou knows the the visitors have nothing to lose after sealing third spot already.
He said: “They have had a strong season and been really solid in that third position.
“Every game against them has been a good game. But we sit where we are because of our own performances and we have had to overcome some pretty determined challenges in recent weeks.”
Meanwhile the Australian is hopeful qualification into the Champions League group stage next season will not only help Celtic in the transfer marker but also also give them more free time pre-season to build a team that can fire on all fronts again in the coming season.
Two of the major successes in the transfer market this season were the loan signings of Tottenham defender Cameron Carter-Vickers and Benfica winger Jota and re-signing them would be significant pieces of business this summer.
Postecoglou said: “We are in discussions with them obviously and, as I have said all along, with these kind of things it’s never a simple process.
“But both had unbelievable years for us and been outstanding contributors and both are really happy here. Our intent is to try and keep them at our football club, but these things need a point where all parties agree.
“I am hopeful we will get to that point, but at this point we are not quite there yet.”