Besic will be on the sidelines for the next six months due to a knee injury.
The 23-year-old Bosnia and Herzegovina international suffered the injury during Wednesday’s Wayne Rooney testimonial match at Old Trafford.
Everton's Muhamed Besic celebrates
Deulofeu hopes that Besic recovers from his injury soon and has posted the following message on Twitter:
Tom Bradshaw (R) in action against Everton's Muhamed Besic
Besic is a talented and promising defensive midfielder, but his career at Everton has been affected by injury problems.
Deulofeu scored two goals and created 34 chances in 26 Premier League appearances for Everton during the 2015-16 campaign.
The Spain international winger will be hoping to get more playing time this season and establish himself as a key player for the Merseyside outfit under new manager Ronald Koeman.