Solskjær began the 1996 Tippeligaen in defeat, losing 2–0 to Rosenborg. However, in his next match on 21 April 1996 against Moss, he scored a hat-trick as Molde won 8–0. He scored a brace against Tromsø on 19 May in a 3–0 victory, and his goal-scoring form led to interest from Hamburg of Germany and Italian club Cagliari. Molde's then-manager, Åge Hareide, made Solskjær available to both Everton and Hareide's old club Manchester City for £1.2 million. However, neither Everton nor City were willing to take a risk on Solskjær, and the interest from Hamburg and Cagliari fell through after Manchester United submitted a bid of £1.5 million during Euro 1996, which Molde accepted. Solskjær made his final appearance for Molde on 21 July 1996 in a 5–1 win against Start, scoring the fourth goal in the 85th minute, before throwing his shirt to the crowd in celebration and receiving applause as he was substituted. He finished his time at Molde with 41 goals in 54 games in all competitions.