Lagerbielke has played 15 league games for Elfsborg this season and has significantly contributed to his side tightening their grip on top spot in the league table.
His robust on-field performances have intrigued the Bhoys, who are set to sell their star defender Carl Starfelt to Celta Vigo.
The Bhoys are keen on replacing Starfelt with Lagerbielke in their backline and have already tabled a bid for the Swedish centre-back.
It has been suggested in some quarters that Elfsborg are considering the bid worth £2.9m for Lagerbielke.
And now it is claimed that Brendan Rodgers’ side are close to being agreed with a potential deal for their defensive target and they are now in advanced talks with the Swedish outfit.
The Bhoys are eyeing marking an impact on the Champions League this season after a lacklustre defensive record in the elite continental competition last term.
And they are hoping that Lagerbielke’s inclusion in their squad will give them a defensive filip moving forward.
Now it remains to be seen how well the Swede will fare under Rodgers’ tutelage in the event of him arriving at Parkhead.
