And the latter newspaper have gone so far as to claim that Fabio Borini will be used as a makeweight to lower the price of the deal.
The Reds have already seen two bids rejected for Lallana after lodging first £20 millon and then £25 million pounds.
That seemed to have spelled the end of Liverpool's pursuit of the 26-year-old however as speculation mounted they were turning their attentions to alternative targets Xherdan Shaqiri and Lazar Markovic.
News that Lallana is still high on the agenda shows that he really is Rodgers' number one transfer target this summer and will do everything in his power to acquire the England international's services.
Liverpool shall continue to monitor Shaqiri especially if chasing Lallana ultimately proves fruitless but the Swiss is probably now seen as a last resort.
Rodgers and owners FSG are prepared to bide their time and that makes sense since the player is keen to go to Anfield, irrespective of Saints chief executive director Les Reed's latest comments.
“Lallana’s been here long enough, we’ve brought him to this level and we feel that perhaps he should give it a little bit longer,” Reed said.
“Anybody seriously considering coming for our players are going to have to think very significantly about the size of the fee.
“If we do take money it will be because it’s the right amount and it enables us to improve the team and move forward.”
“I hope the (managerial) announcement will prick up a few ears and they will think that’s a good, positive move from the club. If players leave, it will be because we believe it is right for the club.”
Lallana is clearly not worth £30 million by anyone's standards but to Liverpool he is worth whatever they are prepared to pay for him so if it ends up being around that figure then so be it.
Rodgers clearly feels the player is ideal for his system, Lallana's profile suited to a high energy and pressing game engendered under Mauricio Pochettino.
Add to that his technical qualities and versatility then Liverpool's refusal to give up the chase can be better appreciated and understood.