Napoli lost to Roma over the weekend putting their qualification for next season's Champions League at risk.
And reports in Italy suggest that Higuain could look to leave if the Serie A club are not playing in Europe's top club competition next term.
Napoli remain in the Europa League this season and could yet qualify for the Champions League by winning that competition.
But Higuain has reportedly told Napoli that he has no intention of taking part in the same competition next season.
Liverpool have been heavily linked with a move for Higuain in the past, but their defeat to Arsenal over the weekend may have handed the Gunners the advantage in the race for the Argentine star.
I'm confident that the team can make third place, then we'll see about Gonzalo's future.
Gonzalo Higuain's agent Nicolas
The Reds are now a doubt to qualify for the Champions League themselves, seemingly ruling them out of a move for Higuain.
Earlier this year, Higuain's brother and agent Nicolas said: "Do Liverpool want Higuain? I don't speak English, just Italian, French and Spanish.
"I haven't spoken to any club, firstly because they haven't called me and secondly because it would be disrespectful to Napoli, it wouldn't be fair.
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"[Napoli President Aurelio] De Laurentiis is a great person, a man of honour and I couldn't behave incorrectly. We're not thinking about leaving Napoli.
"I'm confident that the team can make third place [and qualify for the Champions League], then we'll see about Gonzalo's future.
"I haven't spoken with any team, Gonzalo is calm, he has a contract with Napoli and he's not planning to leave because he's happy. We have to fight for third place."
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