The People says Arsenal boss Arsene Wenger has been searching for a left-winger all summer and was linked with Florent Malouda, before he joined Chelsea, and Marseille's France star Franck Ribery.
But now he has set his sights on Rovers' Norwegian flyer, 25, and he's ready to pull out all the stops to get his man.
Blackburn boss Mark Hughes, however, is a huge fan of Pedersen and has rejected the bid.
And he has told Wenger he will only think about doing business if the Frenchman ups his offer or makes it a players-plus-cash deal.
Hughes sees Gunners striker Nicklas Bendtner and midfielder Mathieu Flamini as potential deal-makers but would still demand a cash sum on top of that pair.