The eight-year-old won three Grade 1 events when in the care of Peter Casey, but Curran has decided to give his star performer a change of scenery.
He said: “He’s going to Tony Martin. Hopefully a move will freshen him up a bit and will be the right thing to do.”
Flemenstar proved a revelation when sent chasing in the 2011/12 season, recording five wins over fences for Casey, including two Grade 1 events.
He started last term in the same sparkling form, winning the Fortria Chase on his reappearance before landing another success at the highest level in the John Durkan Chase.
However, he suffered defeats when favourite for both the Lexus Chase and Irish Hennessy at Leopardstown, before being well beaten by Sprinter Sacre in the Melling Chase at Aintree on what was to be his final start for Casey.
The horse was reported to be suffering from a virus during those post-Christmas efforts and while Curran has now moved the horse from Casey’s yard, he insists it was an amicable split.
He said: “There’s been no falling out, there was never any falling out at all.
“We just thought it was better to move the horse with the idea being it would freshen him up.
“We had some great times with Peter.”
Curran will send Flemenstar to Martin in the next few weeks but has no immediate plan in mind.
He said: “He won’t be going to Tony’s for two or three weeks and there’s nothing planned yet for him.”
Speaking earlier, Casey said: “He’s not coming back. It is disappointing news.”
Martin said he was delighted to be about to train Flemenstar and confirmed that Andrew Lynch will continue to ride the horse.
“It’s great to get him. Stevie (Curran) confirmed it with me so it’s great to get a horse like him,” the County Meath handler told At The Races.
“I’ve seen him from the early days because Stevie is a neighbour of mine. He’s been an impressive horse all the way through his career.
“Stevie always pre-trains him and he’s doing the same. When he thinks he’s ready he’ll let me have him, so when that will be is up to him.
“The vibes are very good from Stevie. It’s been all positive from him.
“I don’t know about plans. I haven’t talked about it. It’s very early days and I haven’t discussed with him other than he said he will send him down shortly.
“Other than that we will have to wait and see what he’s like in a few weeks. We’ll have a chat then and see what we’ll do.
“As far as I know Andrew (Lynch) will ride him. He’s ridden him all these years. He’s a local chap and has done an awful lot of work on him so as far as I’m concerned Andrew will have first call on him.
“Peter Casey has done a great job with him through the years and it’s a credit to him to have got him as far as he did so hopefully we can keep it going.”