The Republic of Ireland defender damaged lateral ligaments in his right ankle when he was fouled by Villarreal's Carlos Marchena in Friday's friendly at Goodison Park.
Though there was initial relief that no bones were broken, Everton sent Coleman for a second scan on Monday to determine how much damage he had sustained.
Pre-season friendly? Seamus Coleman is caught by Carlos Marchena
He would have missed Saturday's Premier League opener at Tottenham as he had a suspension from last season to serve. However, Everton manager David Moyes is facing the prospect of being without Coleman, who has become an increasingly influential figure in Everton's squad, until late September at the earliest.
Head physio Danny Donachie said: 'Seamus has torn the lateral ligament in his right ankle. He will be visiting a specialist in London later this week for further assessment.'
Everton, who will also be without Mikel Arteta for the trip to White Hart Lane, can ill afford to be without any more first-team members, although Sylvain Distin does not expect them to lose Phil Jagielka.
Arsenal have not been in contact withEverton over a move for Jagielka since they had an opening ?12million bid for the 28-year-old defender rejected last month but are poised to return.
Down and out: Coleman now faces a lengthy spell on the sidelines
Distin, though, has not seen any signs from Jagielka that he wants to leave. 'He has not come out and said he wants to go anywhere, so I guess that means he wants to stay,' said the French defender. 'I don't think any players want to leave here,to be honest.
'Jags is an amazing player, you don'tplay for your country if you are not. He's still young and still improving. He had some injury problems but seems to be over them now andis doing great. He's got top clubs after him and that's a sign of his quality.'
Distin has one year remaining on his contract and is eager to remain on Merseyside after holding what he has described as 'encouraging' talks.
'If I feel I have to change clubs then I will do it,' he said. 'I'm quite honest about that. If I don't feel good then I say so. But I do feel good about being here and, if I can stay, then I will.'
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