West Brom have sacked Nicolas Anelka citing "gross misconduct" after the striker claimed on Twitter he had quit the club.
Mauricio Pochettino expects to be at Southampton next season and is looking forward to working with chairman Ralph Krueger.
Steve McClaren has wanted to bring in a new defender since becoming head coach at the Sky Bet Championship club at the beginning of this month and the former England manager made an approach for the versatile Wisdom, who can play at both right-back and centre-half, over the weekend
McClaren made his move after seeing Zak Whitbread, on loan from Leicester, suffer a calf strain during the first half of the Rams' 3-2 league win at Watford on Saturday.
Despite initially forcing his way into Liverpool boss Brendan Rodgers' team, Wisdom has seen his first-team opportunities at Anfield limited this season.
The summer acquisitions of Aly Cissokho, Mamadou Sakho, Kolo Toure and Tiago Ilori have pushed him down the pecking order.
The England Under-21 international has made a total of 22 appearances for the Reds but during the current campaign has played only two Barclays Premier League games, including a solitary start at Swansea, and a Capital One Cup outing.
Wisdom, 20, joined Liverpool's youth set up from Bradford in 2008.
Meanwhile, Derby also thought to be interested in West Brom midfielder George Thorne.
The Rams have limited options in midfield with Paul Coutts, Jeff Hendrick and James Bailey all out with medium to long-term injuries while Thorne, 20, is available for loan in order to boost his fitness following a lengthy absence with a knee problem.