Celtic have outlined possible plans to build new training facilities at their current Barrowfield site in Glasgow but could also re-locate elsewhere.
Peter Lawwell wants the matter solved soon
Celtic chief executive Peter Lawwell said: "One option is to do something with what we've got at Barrowfield and the second is to go to a new site.
"A third option has just been put to us. The second option will take quite a bit of investment.
"We hope to make an announcement within the next two months."
Former Celtic manager Martin O'Neill has long expressed his envy of the Murray Park training facility enjoyed by city rivals Rangers in Milngavie.
"We spend £1.5m a year on youth development, so we have an academy, a structure but no top-class facility," said Lawwell.
"Tommy Burns runs it and we'll just need to bring the facilities along that will match the quality of our coaches.
"We've had kids coming through already and there are more to come. We have excellent ones on our books.
"The thing we'll take into account if we stay at Barrowfield is the whole area around us will be improved.
"Belvidere Hospital will be turned into houses. The new national indoor arena will be built near here.
"Also there will be a motorway link to the M74 built near our superstore and part of London Road will be turned into a pedestrian precinct.
"One of the other options would be a world-class one.
"The subject's an irritant and it will be good for everyone once a decision has been made and we can get on with things."
Meanwhile, the Hoops will not travel to America as part of their pre-season preparations this summer.
Celtic have played in the Champions World Series in the US with glamour matches against Chelsea, Manchester United, Liverpool, Roma and AC Milan over the last two years.
But, with new boss Gordon Strachan still finding his feet at the club, Celtic are reluctant to make the long trek across the States this summer.
"We aren't going to the States now," he said. "We might go down to the London area and play Fulham and another game down there."