According to the Liverpool Echo's James Pearce, reports in the Spanish media suggested the former Real Madrid goalkeeper has signed a pre-contract agreement with the Reds, but Pearce said the club are "baffled" by the rumours.
Casillas will be a free agent this summer when his contract with FC Porto expires.
Per Pearce, bookmakers suspended their betting on the 36-year-old moving to Anfield, but Reds boss Jurgen Klopp is "adamant" he will not be signing goalkeeping reinforcements this summer.
The German brought in Loris Karius last year to compete alongside Simon Mignolet and Danny Ward, and he believes Liverpool are sufficiently stocked between the sticks.
Casillas was once among the best in the world and has made over 700 appearances for Real and earned 167 caps for Spain.
The Spaniard is no longer in that category, with errors creeping into his game more as he's aged.
Nevertheless, Football Whispers' Sam McGuire believes he could be a worthwhile signing for the influence he would have on the squad:
Indeed, at this point, Casillas would be more useful behind the scenes at Anfield than he would on the pitch. Not only has he declined, Mignolet has also shown good form of late, per football writer Joseph Musker:
Neither he nor Karius has convinced over a long period at Liverpool, but if Mignolet can carry this form into next season, the Reds won't need to try to rectify the situation with more recruitment.
If Liverpool were looking for an upgrade on Mignolet in the transfer window, then Casillas would be a risky choice even on a free transfer.