Barmby was former manager Terry Venables first signing as Leeds United manager, joining the club for £2.75m from Liverpool in August 2002.
United are understood to be handing Barmby a pay-off of around £1m but will save a further £2m in wages over the remainder of his contract.
Barmby made just 31 appearances for Leeds and is now expected to join his hometown club Hull City.
Tigers manager Peter Taylor told the club's official website: "We're very close with Nick and I've had quite a few chats with him recently. I've also known him for a few years but didn't realise he played for England against Italy when I was in charge for that one game!
"But he played well to be fair and I'm really hopeful it's going to happen. If Nick does join us it's all for the right reasons. He's had a frustrating time at Leeds not playing many games and he's a great lad and a good professional.
"Nick will only want to come to us to be the best player on the park and that's why I'm interested in him. He's very, very keen and hopefully we can get things sorted."
He added: "Nick Barmby is still a Premiership player, there's no doubt about that. In a normal situation we couldn't afford anybody like that but now we've gone up a level, Nick had a frustrating time at Leeds and he's from this area where his family is very settled.
"I was born in Southend and if somebody had said to me you could get yourself financially secure and then go and try to achieve something with your home town club it's something I'd have been very interested in.
"Nick's definitely got the bit between his teeth and would like to help take this club to the next level."