ESPNcricinfo understands that Kings are expecting Livingstone to arrive on April 10, the day after their fixture in Hyderabad, while Livingstone said on Thursday afternoon that he is hoping to get clearance to travel from the ECB "over the next 48 hours or so".
"[I'm] getting there, finally," Livingstone said on LancsTV's coverage of Lancashire's opening County Championship fixture against Surrey. "It's been a long road: three or four days a week at the gym over the last three or four months. Maybe towards the end of this week, or start of next week, I'll fly out to India and get going again.
"Feeling much better. I had some injections midway last week. It's settled it down a lot, finally been able to get outside and do some running and get back to proper cricket stuff. That's probably been about four or five days now, so just trying to build back up to match fitness now.
"I got over my ankle to play in the World Cup, then my knee has been a bit of a niggly one. I finally sorted that out and my ankle flared up again. Hopefully they're both under control now and it'll be nice to get back playing finally. It's been a difficult couple of months, but finally now I'm like a little kid wanting to get back playing cricket again."
Livingstone said that detail of his specific travel plans is "the million-dollar question" but that he is hoping for ECB clearance imminently. "Hopefully over the next couple of days, I'll get the clearance to head out there," he said. "I'm really looking forward to getting back out, getting back playing, and hopefully over the next 48 hours or so I'll finally get that."
Livingstone was retained on a contract worth INR 11.5 crore (£1.15m approx.) after a strong first season with Kings in 2022, in which he scored 437 runs with a strike rate of 182.08 and chipped in with six wickets, and is expected to slot into their middle order.
Kagiso Rabada has arrived in India this week and will be available for Sunday's fixture in Hyderabad, while Matt Short - who replaced the injured Jonny Bairstow in Kings' squad - is the other overseas player they have available to them as things stand. Franchises are allowed up to eight overseas players in their squad, but Kings signed only seven for 2023.
Rajapaksa retired hurt on Wednesday night after he was struck on the forearm by a shot from Shikhar Dhawan, while standing at the non-striker's end, but should be available on Sunday if required. He tweeted later that night: "The X-rays have cleared me of any broken bones/fractures! Plenty of ice needed but I'm doing fine."
Livingstone has become an important part of England's white-ball set-up over the last two years and is likely to feature in their defence of the 50-over World Cup in October-November. He believes that exposure to Indian conditions will come in handy ahead of that tournament.
"You're seeing so many English lads in the IPL at the moment, gaining great experience," he said. "I spoke to Sammy [Sam Curran] last night actually, after the game. He said the ball was like a bar of soap, and you don't quite realise at the time but that's such a good experience for not only Sam but for England moving forward in eight months' time; it might be like that in a World Cup semi-final or whatever.
"It's a great experience for the lads that are out there at the moment. Hopefully that sets us up well; we've got loads of lads out there which is great: we've got a really well-balanced team at the moment, we've got a lot of talent within our group. We've got a great environment and everyone loves being around each other, so hopefully, India will be good towards the end of the year."
Matt Roller is an assistant editor at ESPNcricinfo. @mroller98