Inzaghi has Inter on the brink of a Scudetto triumph this season, while he also led them to last season's Champions League final.
The Athletic says the Reds are monitoring Inzaghi's situation at Inter coach as they prepare for Jrgen Klopp's end of season departure.
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However, Inter will fight hard to keep hold of their coach.
But things could change dramatically if Inter owners Suning fail to pay the loan they took out from Oaktree. The deadline is due this summer.