The Sky Blues saw a £2.5m bid turned down by the League One outfit last month - with the fee rising to £3m.
This week, they increased their offer in a £4m package, but were rebuffed. But they have refused to be put off and have signed the Reds captain before the deadline after coming in with a renewed offer.
It is under £5m, with the player understood to be undergoing a medical on Friday evening after a fee was agreed.
Speaking recently at a fans' forum, chairman Neerav Parekh said that the player would 'definitely' be staying, but the size of the offer, right at the end of the window and the player’s desire to leave, has prompted a rethink.
Kitching missed the Reds' weekend win at Wigan with a groin issue which has been affecting him in the early part of the season.
Barnsley have brought in left-back Owen Dodgson and central defender Jamie McCart and are also understood to be looking at bringing in another defender before the deadline.
Asked about Kitching at his pre-match press conference on Thursday afternoon, Reds boss Neill Collins said: Collins continued: "Based on the things I've heard up to this point, I am confident he (Kitching) will be a Barnsley player, but again we have all been in the game long enough to know that things can change.
"Until that window shuts, I will just try and stay level-headed about that.
"We have got some very good players and when you have got some very good players in football, there's interest from teams higher up. The club obviously have expectations that have to be met for any player to leave.
"If not, they will be here and an important part of the club going forward."
Kitching's previous club Forest Green Rovers are understood to receive a sell-on fee as part of the deal.