The Serie A side submitted a new €45 million (£39m/$42m) bid for the Nigeria international, according to Calciomercato, following the rejection of their initial offer.
CEO Beppe Marotta described this week as “crucial” for deciding the winger’s future and warned that Inter could walk away if no agreement is reached.
"I won’t deny that Lookman is an important player. He’s a player we didn’t discover ourselves; I think he’s on the radar of every Italian and European sporting director,” Marotta told the media.
“But today he’s an Atalanta player. I’ve spoken a few words with Luca Percassi, but it’s premature to say what will happen.
"This will be a crucial week for Lookman. We're looking for a player who can bring unpredictability to Inter, and Lookman is one option, but not the only one. If we don't reach a conclusion in the next few days, we'll make a different choice."