According to RMC Sport, the 33-year-old is close to agreeing terms with Monaco but has not shaken hands over a deal.
The two other clubs who have a chance of signing the hard-hitting midfielder are Brazilian side Flamengo and Rangers.
Steven Gerrard added Ryan Kent to his squad on deadline day and the experience of Marchisio would be a welcome addition.
Kent’s £7million signing has been slammed by Celtic hero Chris Sutton, though, who believes it reeks of panic.
Claudio Marchisio left Zenit St Petersburg in July (Image: Getty)
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"If Rangers signing the winger from Liverpool wasn’t down to sheer panic in the wake of the defeat to Celtic last Sunday, then I don’t know what is," he told the Daily Record.
“Kent is a good player. I even suggested at the end of last season that Celtic should try to get him to boost the squad.
“But it seems that, in the eyes of the Rangers supporters, Kent’s signing is a game-changer.
“The last-ditch transfer window strike which is going to tilt the title odds back in their favour.
“At best, that is optimistic. At worst, it’s bordering on hysterical.”
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