A string of injuries and Iversen's recent lack of success for Premier League clubs Tottenham and Wolverhampton led him to come home and recuperate in Norway.
His presence helped lift Vålerenga to the top of the domestic league and Iversen is again a key player for Norway's national squad.
Iversen, who played for Rosenborg before seeking his fortune in England, now wants to resume his career abroad but has not ruled out staying in Norway. Now Rosenborg are officially interested in getting him back from Vålerenga.
"A healthy and motivated Steffen Iversen is always welcome at Lerkendal (Rosenborg's stadium). He knows we are interested," Rosenborg coach Per Joar Hansen told newspaper Adresseavisen.
"If Steffen gets an offer from a good foreign club he will leave. If he stays in Norway it is up to him and his wife. They must decide where they want to live," Hansen said.