Napoli president Aurelio De Laurentiis says he has offered Manchester United one million euros to play his side in a friendly game.
The proposal - worth £880,000 - is for United to play at the San Paolo stadium in Naples.
The Serie A outfit want to raise their international profile and hope the English champions will accept the invitation.
Speaking at a press conference on Tuesday, De Laurentiis said: "I have offered Manchester United one million euros to come here and play a friendly against Napoli. I am awaiting a reply.
"My aim is to bring Napoli to be among the top teams, not just in Italy, but at international level.
"There is a lot of work to be done."
Meanwhile, Uruguay centre-back Miguel Angel Britos has joined Napoli from Bologna for an undisclosed fee.
The 25-year-old makes the move having notched up 70 league appearances for the Rossoblu since his 2008 arrival from Montevideo Wanderers.
Ligue 1 club Lyon were thought to be interested in his services but Napoli have won the race for his signature.
"I am delighted to have arrived at Napoli," said Britos.
"I've come to a big club and here I can make the leap in quality that I always dreamed of. (Coach Walter) Mazzarri wanted me here and I hope I can soon repay his trust."
Napoli are also close to completing the acquisition of Argentinian winger Mario Alberto Santana, who is available as a free agent after leaving Fiorentina earlier this summer.
Santana could become Napoli's third signing in the space of 24 hours after the club unveiled Swiss midfielder Gokhan Inler on Monday.