According to talkSPORT, he Premier League side hope that Gerard Houllier, the former Reds boss and current global sports director at Salzburg, will be willing to talk business.
After scouting Berisha for a matter of months, Brendan Rodgers has now opened talks with the Austrian side over a possible deal.
The former Egersund and Viking player was watched by Anfield representatives during the surprise 3-0 friendly victory over European champions Bayern Munich last weekend, while Liverpool also scouted him during their 4-0 league win over Austria Wien last month.