Alex Oxlade-Chamberlain is waiting for Liverpool to return with an improved offer after Arsenal rejected a bid of around £30m for the player.
The Evening Standard have reported that the Reds are hopeful of doing a deal for under the £40m agreed with Chelsea, after Oxlade-Chamberlain made clear his preference to move to Anfield.
The Premier League champions had expected to complete the signing before the close of the transfer window, but that has grown increasingly doubtful due to concerns as to where he would fit into the team.
The 24-year-old is believed to want to be utilised as a central midfielder, but Chelsea boss Antonio Conte has offered him a role as a right wing-back.
Oxlade-Chamberlain is reportedly more confident of being played in his preferred position at Liverpool, although it remains to be seen whether the Merseyside club will meet Arsenal's demands.
The Gunners are willing to keep the England international if his valuation is not met, and he could be set to see out the final year of his contract at the Emirates.
Oxlade-Chamberlain is also said to see Liverpool as a more secure move due to speculation over the future of Conte and uncertainty over the club's transfer business this summer.
It is not yet clear whether Liverpool will stretch to Arsenal's demands for the player, or whether Oxlade-Chamberlain will eventually opt to join Chelsea. The Evening Standard claim that "all outcomes are possible" with just one day of the transfer window remaining.