The Toffees are expected to get through their play-off with Hajduk Split, while Ajax and Athletic Bilbao are among the other strong favourites in Thursday's ties.
All three teams can be backed at a boosted treble price of 5/2 (3.50) with dabblebet, which could prove to be stunning value for Thursday's matches. At the current prices the bet pays 23/10 (3.30),
Ronald Koeman has invested heavily in his squad so Everton can cope with the rigours of continental competition and qualifying for the Europa League group stage is a priority.
Although there will be no Ross Barkley due to injury, Koeman's new-look Everton should put themselves in a strong position with a first leg victory over Croatian side Hajduk Split, who have taken a decent return of 10 points from the first five league games of their new season.
Ajax scraped past Ligue 1 side Nice on away goals after two draws in the last round but Rosenborg should provide a more straightforward test in the play-offs.
Rosenborg have lost six of their last seven matches in the Europa League so their continental record is poor, although a 2-1 loss to Heracles at the weekend was slightly worrying for Ajax.
Completing the 5/2 (3.50) treble with dabblebet are Athletic Bilbao, who go away to Panathinaikos of Greece on Thursday.
The hosts won both legs against Qabala in the last round but Athletic are a clear step up in class, although they have a new coach in Jose Angel Ziganda, who replaced Ernesto Valverde after he succeeded Luis Enrique at Barcelona.
Aritz Aduriz is in the twilight of his career but the veteran striker will be determined to thrive on what could be his last season in European football, with the 36-year-old backed to see Athletic to victory.