It was suggested the club were interested in the former Chelsea boss, even though Rodgers is currently in situ.
But Liverpool say such a move would be out of character with the way American owners Fenway Sports Group have run things so far.
Elsewhere, memories of Lansdowne Road and 2001 will be rekindled at Old Trafford tonight.
Louis van Gaal and Mick McCarthy renew acquaintances as Manchester United face Ipswich in the third round of the Capital One Cup.
Kick off in that one is at 8, as it is at Anfield.
The rest of tonight's games have 7.45 starts, with a North London derby meeting of Tottenham and Arsenal the potential highlight.
Jose Mourinho takes his Chelsea side to Walsall, and Southampton face a tricky trip to M-K Dons.
Elsewhere, Newcastle take on Sheffield Wednesday, Crystal Palace entertain their former tenants, Charlton, and Norwich face West Brom.
