Britain's Got Talent Dog Turns Down American Idol Invite

Sources tell TMZ ... Pudsey the dog and 17-year old owner Ashleigh were asked to appear live on the "Idol" stage -- it's unclear if they would perform -- but when producers called about the potential gig ... they were met with a big, fat NO.

The reason behind the rejection ... we're told Pudsey and Ashleigh have been getting offers round-the-clock since winning the UK's talent competition ... and the pair is literally too busy to squeeze in an "Idol" appearance.