The Reds saw a £20million bid for the England international rejected last week and were told to up their offer to at least £30m.
But Rodgers is unwilling to meet that price-tag knowing he could go elsewhere for a cheaper player of the same ilk as Lallana.
And it’s believed that player could be Bayern Munich’s Shaqiri, who has been regularly linked with a move away from the Allianz Arena since signing for them in 2012.
The 22-year-old Swiss international could be available for around a third of the price Lallana would cost the Anfield outfit, and would likely welcome a move to the Premier League.
Meanwhile, Rodgers has admitted that the lure of Champions League football has given his transfer activity a welcome boost this summer.
He said: “The big lure will be Champions League, that’s what I’ve found in my conversations with agents and people.
“The best players want to play in the big competition.”