Spurs boss Harry Redknapp, however, claimed he will not be loaning Keane out again which means Celtic would have to come up with a substantial transfer fee if they want to keep him in Glasgow.
However, Celtic boss Mowbray ruled out a permanent deal ahead of the Scottish Premier League clash with St Johnstone at Parkhead.
"For me it is about Robbie enjoying his football and hopefully the Celtic fans have enjoyed what he brings and the goals that he brings," he said.
"If it is the case that he goes back to Tottenham at the end of the season all we can do is hope he enjoyed his time at Celtic and contributed some goals, which he already has done, and hopefully some enjoyment for the supporters.
"But football is very much about finance these days and Robbie Keane is way out of our structure.
"He cost them (Spurs) £12million. I don't think that our board are going to loosen the purse strings that much.
"I wouldn't dare tell Harry Redknapp what his best options would be, but I do know that Robbie will have benefited from playing regular football and he has shown the quality that he possesses.
"Harry has some pretty special players at his disposal and Robbie is here because Jermain Defoe, Peter Crouch and Roman Pavlyuchenko were competition for him and obviously he wanted to play. He may face similar challenges when he goes back.
"But when was the last time a Scottish club played £12million for a player? Was it Tore Andre Flo? Those days are long gone in the Scottish game, I think."
Celtic have beaten Saints 5-2 at home and 4-1 away this season but Mowbray is expecting a difficult afternoon against a side he believes might have surprised some people by moving to within three points of sixth-placed Hearts with two games in hand.
"They were tough games for us until we got the goals to win the match and it will be the same at the weekend," the former Hibernian and West Brom manager said.
"I'm sure they will give us a stern test. They have been very competitive this season and their results over the last couple of weeks highlights that.
"Some people might have thought they would have been clambering for points to stay out of the relegation zone and yet, there they are, trying to get into the top six, which is a great credit to them.
"Whether they can or not, we will wait and see but they will come to Celtic Park in confident mood."
Marc-Antoine Fortune is hoping that Mowbray is aware of his scoring record against the Perth side this season when it comes to picking his starting XI.
The former Nancy striker, who was on the bench for last week's Active Nation Scottish Cup win at Kilmarnock, has grabbed a brace in both games against the Perth side and believes that St Johnstone can be considered his "lucky team."
He said: "Yes, sometimes you do score against the same teams. I scored at Motherwell for Nancy and I also scored there for Celtic.
"Sometimes you get the chance to score against the same team and I hope Saturday will be the same.
"But I don't have to say that (to the manager), he makes his choice."
Celtic had to come back from a goal down at McDiarmid Park in January before running out comfortable winners and Fortune is hoping this time they make things easier by taking the initiative.
"I hope we don't wait until they score first and then we have to come back to win the game," he said.
"I hope we score first and then kill the game with a second goal. We have to be prepared and we have been working hard at training.
"We won our last game in the cup against Kilmarnock and we have to keep going, that is what you have to do at Celtic."
Celtic v St. Johnstone. Click here to bet.