The duo have both been handed plenty of chances over pre-season by new Everton boss Marco Silva.
Besic and Dowell were loaned out to the Championship last season, with the former joining Middlesbrough and the latter spending time with Nottingham Forest.
The Everton duo both impressed on their temporary spells and have been given plenty of opportunity to impress over pre-season since Silva came in.
Both Besic and Dowell have featured regularly in Everton’s friendlies, and Silva admits he has a close eye on the pair.
He said: “I did my analysis, but it is my obligation to be fair with all the players too.
“After analysing them and watching them I can start to take my decisions on them. Of course some of them were on loan last season. Besic was one of them, Kieran as well – and some more.
“But now is the moment for me to see all of them in training sessions daily and in the games as well because sometimes that is different than in the sessions and for me it is important for me to see them.
“The younger players really want to play in our club – and for me that is the most important thing.
“Whether they have quality or not you also need passion and they have big passion for our club.”
Besic and Dowell both may want to stay with Everton for the upcoming campaign, but whether they will be kept around remains to be seen.
Besic has plenty of competition for places in defensive midfield, while Everton’s attacking options are set to increase from the arrival of Richarlison, which could put another obstacle in Dowell’s path.
Everton lost their latest pre-season friendly 1-0 against Porto, with Besic and Dowell both featuring during the contest.
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