Doucoure missed Monday’s Premier League defeat at Chelsea after coming off during the win at West Brom on 4 March.
Everton Carlo Ancelotti said he was “hopeful” Doucoure could return before the end of the season.
The Italian also confirmed playmaker Rodriguez would not be available until after the March international break.
Rodriguez had been playing with a calf issue before missing the past three games.
It means the 29-year-old will miss Saturday’s visit to Burnley and the FA Cup quarter-final at home to Man City on 20 March.
“James played well, really well, against Man United and against Liverpool but he was not 100% fit,” said Ancelotti.
“We decided to give him a proper recovery and don’t let him play at 70 or 80%. We have taken this decision together and the player agrees.”
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