His club, Molde, want around pounds 700,000 for the 23-year-old former Norwegian Under 21 international, but he left for home still undecided.
Other British clubs are also showing an interest in Rudi, who the Saints manager, Dave Jones, believes will add much-needed flair to his midfield.
Saints already have Egil Ostenstad and Claus Lundekvam on their staff and they were joined by fellow Norwegian Stig Johansen last week. Johansen may make his full debut in the Premiership match at Manchester United today after coming on as a substitute against Bolton.
Jones will choose between Johansen, his pounds 550,000 signing from Bodo-Glimt, and Micky Evans, who was one of several Saints players to disappoint.