Icelandic international Sigurdsson looked certain to follow the Northern Irishman to Merseyside after starring for him on-loan at Swansea last season but is rumoured to be on the verge of completing an £8 million move to Tottenham Hotspur.
That deal will go through once Andre Villas-Boas is appointed as the new manager at White Hart Lane meaning Rodgers will turn his attentions to Davies having held a long-standing interest in the 24-year-old and considered signing him when in charge at the Swans.
Wanderers manager Owen Coyle will struggle to hold onto his star players after dropping into the Championship last season and will sell the attacking midfielder for the right money having already brought in Keith Andrews as a replacement.
The Trotters were relegated from the Premier League last term after 10-years with Davies proving to be a shining light scoring four times and convincing Rodgers to splash £6m on him.
He’s yet to make his first signing for the Reds since taking over from Kenny Dalglish at the start of June with the European Championship’s in Poland and Ukraine making it difficult to complete any deals.
There has been speculation that Rodgers is keeping tabs on Victor Moses situation at Wigan Athletic and is mulling over whether to make an offer for the Nigerian international.
Moses was the subject of a failed £4m bid from Chelsea last week that caused Latic’s chairman Dave Whelan to query whether the Champions League winners were ‘taking the mickey’.
The 22-year-old’s contract runs out next year and, with former club Crystal Palace due 20 per cent of any transfer fee, Whelan will only accept a bid of £8 million to let his prized asset leave.