The News of the World says the Anfield club rejected a cheeky £15m bid from the Gunners during the summer.
But after a howler by cock-up keeper Manuel Almunia gifted West Brom a 3-2 win at the Emirates, Arsenal are considering a new bid in the January transfer window to solve their long-standing goalkeeper problem.
Reina, 28, was the keenest of all Liverpool's stars to quit Anfield after a season of turmoil on and off the pitch.
But the club regarded Arsenal's bid as far too low.
Now Liverpool, humbled by League Two Northampton in the Carling Cup last week, are facing another lurch towards financial disaster.
The deadline for Hicks and Gillett to renegotiate their £282.4m bank loan is due to expire next month.
And unless something dramatic happens in the coming weeks, Liverpool will be in a much weaker position to resist bids for their star names.