Laudrup has turned Getafe's fortunes around since taking the reins in 2007, leading the Spanish minnows to the quarter-finals of the UEFA Cup and the final of the Copa del Rey.
But Tutumlu claims the Danish coach feels the time is right for him to move and told Globo FM: "Laudrup's cycle at the club has ended. It has already been a month since he told (Angel) Torres (Club President) to look for a new coach for next season."
Getafe have had modest success in the league this term - they lie 13th with one round of matches remaining but have enjoyed victories over Barcelona and Primera Liga champions Real Madrid.
But it is in cup competition they have excelled with Laudrup's attacking style sweeping past Tottenham, Anderlecht, AEK Athens and Benfica.
The club came within five minutes of progressing to the semi-final, but two late goals saw German giants Bayern Munich go through on away goals after a 4-4 aggregate score.
Laudrup played in Spain for seven years, winning four consecutive Primera Liga titles with Barcelona followed by another with Real Madrid and would love to continue working there.
The 43-year-old was heavily linked to the Barca job, before another former Nou Camp hero - Josep Guardiola - was elected to replace Frank Rijkaard at the end of the season.
Tutumlu insists there is no shortage of opportunities for Laudrup but believes the former Brondby coach will opt to take over the reins at Sevilla.
"Spain is like a second home, his family are very happy here," he said. "If he stays it will have to be a team big enough for Michael. Sevilla is and why not?"