LONDON, March 23 (Reuters) - The dollar index is not far from fair value but it is unclear how much more the U.S. currency will strengthen against the euro, St Louis Federal Reserve President James Bullard said on Monday.

Speaking on CNBC, Bullard also said an exit of Greece from the euro would be possible but prove very painful for Greece itself.

“I think it’s (Grexit) much more manageable than it would have been a couple of years ago and so I do think it could be done but I don’t think it’s advisable to try to go down that path,” he told CNBC in an interview.

“Greece would face a very different and I think bleak future if it went in that driection but i don’t think the spillover into international markets as it would have been.”

On the dollar, Bullard added: “I think it’s unclear at this point where the dollar euro exchange rates are going to go.” (Reporting by Anirban Nag, Karin Strohecker, Marc Jones, Emelie Sithole-Matarise; writing by Patrick Graham)