Miller, 27, moved to Celtic from Wolves on a free transfer last summer but struggled for goals in his first season.

Celtic signed Scott McDonald and Chris Killen earlier this summer and also have Jan Vennegoor of Hesselink, Maciej Zurawski and Derek Riordan as attacking options.

Ironically, Miller hit three goals in his two appearances for the Hoops this season before suffering a hamstring injury.

Strachan said: “He has been fantastic for us. Even when he was not at his best he was a great team-mate, good in the dressing room and he showed earlier in the season what a good player he is.

“Being a good greedy man I don’t want any of my players to move on but sometimes we have to balance the books.

“Football and football management is all about disappointment, you just have to handle it.

“We have a good strike-force but as a manager you like to have as many good players as you possibly can.

“Sometimes that’s not possible for reasons; the players need to play or the books have to be balanced.

“I’d like a squad of 30 but as people keep telling me, it’s very hard to keep 18 happy never mind 30.

“A manager is never happy. We don’t want anybody to go but we want to collect players at the same time.

“So you are never totally happy. But I’m comfortable with the spirit and enthusiasm of the club just now.”

Rumours swept Glasgow that Shaun Maloney was set to return to Celtic Park just six months after signing for Aston Villa, but Strachan was reluctant to discuss potential deadline-day signings.

The Celtic boss laughed off claims that the Parkhead club had been offered £9milllion for Scott Brown before Wednesday’s Champions League qualifier against Spartak Moscow.

Asked if the report was true, Strachan said: “I don’t think so.”