Deeney insists Toney is the best backup option for England and Bayern Munich's Harry Kane.
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"I think that's a personality clash, isn't it?" Deeney said on talkSPORT. "I think the fact that he's said that is immature and stupid anyway, in my opinion.
"What he's letting you know there, is he's probably going to go to the tournament with two (strikers), Harry and Ollie Watkins, potentially three with (Liam) Delap at best.
"And if any problems happen, he's just going to rotate any of those guys up front and then if we lose, guess what, the excuse is already built in, we didn't have enough strikers."