The 25 year old striker struggled to settle with the Latics and endured a difficult first few months with the club following his £5 million arrival from Estudiantes.
He has been on loan with Genoa since January and this weekend scored his first goal for the club against Sampdoria.
Now, Boselli is hoping to remain in Italy beyond his present loan deal. His agent, Jose Iribarren said: "Mauro has a contract with Genoa until 30th June, and the club has an option for take him definitively," Iribarren told calciomercatoweb.it.
"Is the price set at €7million? It is a little less. Mauro would like to remain in Genoa, but right now I don't think there has been a meeting between the clubs. "We hope that they buy him, because he is very happy with his team-mates, the club and the city."