The Brazilian striker was sent off during Chelsea’s 2-0 FA Cup quarter-final defeat by Everton on Saturday afternoon after clashing with Gareth Barry.
Costa has earned a reputation for his combative playing style since arriving at Chelsea from Atletico Madrid.
However, former Sky Sports presenter Keys believes that Chelsea would be better off without the controversial forward.
Writing in his personal blog, Keys said: “A word on Diego Costa. What a fool. The sooner he leaves Chelsea and our league the better. He’s not top class anyway.
“His behaviour is a tedious as Mourinho’s could be at different times. Thank goodness Jose wasn’t around at the weekend to defend Costa.
“Costa doesn’t play ‘on the edge’. He plays ‘over the edge’. He’s boorish. His behaviour borders on that of a thug.
“Some of his antics would see him arrested in the street.
“He owes Gareth Barry a huge debt for ‘confirming’ that he didn’t bite him. He was going to – of that there’s no doubt. TV evidence proved it.”
Chelsea’s loss at Everton followed their disappointing Champions League exit at the hands of Paris Saint-Germain last Wednesday night.
Guus Hiddink’s men now turn their attentions towards their home clash with West Ham United at Stamford Bridge in the Premier League next Saturday afternoon.
Chelsea are currently 10th in the Premier League table after winning the title and League Cup under Jose Mourinho last season.
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