Both players started in Sunday’s 2-0 World Cup qualification win over Albania as Gareth Southgate named a surprisingly conservative midfield against the Balkan nation.
But going forward, Deeney believes that there is no reason why the Three Lions should deploy two holding midfielders against poorer sides, and has suggested that given a choice between Phillips and the West Ham man, Southgate will back the latter.
Speaking on talkSPORT, he said: “There’s no need to have two holding midfielders, especially if you look at the last two games, but I think when you come to the better teams, you’re always going to see a two.
"The pressure will be whether Jordan Henderson can make it or not, whether he can be fit. Mount’s certainly got the legs.
“I think you’re looking at Phillips as well from Leeds – he’s got the legs and he’s got that nastiness in him.
"But Declan [Rice] is going to be the one who is the constant – not only this season, but last season as well, he’s just grown and grown as a player. He’s a wonderful human being.
"It will be interesting to see how he does in the Euros, and whether that solidifies somebody from the top clubs paying the £50-60 million it takes to get him”.
In Sunday’s match, Rice completed 49 passes more than Phillips, made two interceptions more, but won two defensive duels fewer than the Leeds man.