Tambellini has been GM of the team since 2008.
He's currently looking for a new head coach. Tom Renney's contract wasn't renewed after the season.
The Oilers haven't made the playoffs since reaching the Stanley Cup final in 2006.
Edmonton has the first overall pick in the NHL draft later this month for the third straight year.
They made Ryan Nugent-Hopkins and Taylor Hall the No. 1 selection in the previous two drafts.