Inter boss Mourinho wants to transform the club that has won four consecutive Serie A titles into champions of Europe.
Van Persie is currently negotiating a new contract with the Gunners.
He has two years remaining on his current deal, but the Arsenal hierarchy are keen to seal a new deal now rather than allow time to go by and face the threat of him leaving as a free agent in 2011.
Inter know that they will face a massive challenge in prising van Persie out of the Emirates. His wife Bouchra is expecting their second child and the family are settled in London.