Coventry boss Mark Robins has brought in three centre-backs this summer but still believes he needs another one before the window shuts.
The Sky Blues boss has his eyes set on Barnsley’s Kitching, who is considered an important part of the Oakwell squad by Neil Collins.
Last season, Kitching featured 48 times in the league and played a major role in helping the Oakwell outfit reach the League One playoff final.
Coventry City submitted an initial bid of £2.5m which was rejected by Barnsley.
However, the Championship outfit are keen on him and have submitted a new bid for the 23-year-old defender.
Coventry City’s improved offer is £4m, however, the bid failed to match Barnsley’s expectations, and they have decided to reject it.
With less than 48 hours remaining in the transfer window, it remains to be seen whether Coventry will go back with an improved bid.