Barât confirmed the news from Bangkok, where Doherty is currently undergoing rehab treatment for drug addiction.
"Pete's in a great place. We're in a great place," he told NME. "I'm gonna keep popping out and seeing how it is going, show him a bit of support. This is only day two, so let’s see how it goes. It's relaxed."
The singer, who has also formed new band The Jackals, added that the trip got off to a bad start when his guitar broke en route to Thailand.
"I got a new one but right now the sound is two nylon string guitars – I don't think that’ll make it to the record," he said.
Barât and Doherty are busy "going through old tracks and new bits and bobs" but are determined to let the tracks "dictate their own sound".
"We were both reminding each other of scores of tunes that we'd forgotten that had never seen the light of day," Barât continued. "But Plan A is to write new things.
"There's about five new tunes on the work bench at this stage and that's just from having been in each other's company, not even sitting down to write."
Barât also dropped the "working title" of one song, "Woke Up Again", but nothing has been confirmed.
The pair remains convinced that the chemistry between them is still alive and well. "Genuinely, in my hearts of hearts, I know that none of that is lost and we'll pick up where we left off," Barât said.
Barât released details of The Jackals' debut album yesterday, confirmed that it will be titled Let It Reign and released on 16 February following a UK tour.
The Jackals also unveiled a video for their first single, "Glory Days", made in memory of the 306 British and Commonwealth soldiers shot for desertion during World War I.
The band members were recruited last year after Barât posted an ad on Facebook for a drummer, bass player and rhythm guitarist.