A report in The Independent on Wednesday suggested that Gerrard, who left to play for Los Angeles Galaxy at the end of last season after 17 years with Liverpool, would train with the Merseysiders following his return to England this week and could possibly play again on loan or even following a transfer.
Klopp, though, is expected to dampen down the speculation about a dramatic return when he addresses the media later on Wednesday ahead of Thursday's Europa League game away to Rubin Kazan.
Gerrard, 35, admitted in a recent autobiography that he would have stayed at Anfield had he been offered a chance to start coaching there while continuing to play.
He said earlier this week that next year could be his last as a player.
(Reporting by Steve Tongue. Editing by Patrick Johnston)
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