French media outlet FootMercato
Southampton have already signed a centre-back in the form of Jan Berdnark from Lech Poznan for £5m.
However, it seems as though new boss Mauricio Pellegrino is looking to Abdennour as a possible replacement for Virgil van Dijk if he decides to move on this summer. Reports have claimed though that there are a long list of clubs vying for the 27-year-old's signature.
Olympique de Marseille and Newcastle had been previously linked, although it now seems that Leicester City and Inter Milan have joined Southampton as the front runners for the Tunisian's signature.
Leicester have also signed a centre-back this summer in the form of Hull City's Harry Maguire, although Craig Shakespeare could be looking to replace both his current ageing centre-backs, Wes Morgan and Robert Huth.
Despite being linked with a move to the Premier League last summer, the Tunisian international stayed an extra season at Valencia but only made 14 appearances over the last campaign.
Now an exit from the Spanish club, who finished 12th in La Liga last season, seems inevitable and the chance to play in England is thought to be an attractive proposition for Abdennour.
However, there is little chance of Abdennour arriving for a bargain price despite his lack of appearances for the Spanish club.
Abdennour still has three years left on his contract and Valencia paid over £18m for him just two summers ago, so a fee of around £15m is thought to be wanted by Valencia.
No firm offers have been put on the table as of yet, however, if Virgil van Dijk makes a move away from Southampton, it wouldn't be too outrageous to suggest a bid from the Saints for Abdennour could be quick to follow.