Kevin Mirallas and Morgan Schneiderlin and were left out of Everton's squad on Sunday after being involved in an incident at the club's training ground a day earlier, according to reports.
Winger Mirallas and midfielder Schneiderlin were missing from the matchday 18 as the Toffees beat Watford 3-2 at home in the Premier League.
It has been suggested that on Saturday the pair's involvement in a session at the club's Finch Farm complex ended early after their attitude was questioned by coaching staff.
This season has seen Schneiderlin notably struggle for form and Mirallas make just one Premier League start, an appearance that ended with him being substituted at half-time, just over a week ago when Everton lost 2-0 at Leicester.
On Sunday the Belgium international posted a message on Instagram, which has subsequently been deleted, that said: "Thank you for all your messages. It's a difficult situation for me.
"But in life there are things much more serious than my personal situation."
Meanwhile, Everton left-back Leighton Baines has praised David Unsworth's efforts as caretaker boss, stressing the win secured on Sunday was "the least" he has deserved.
Unsworth stepped up from the under-23s two weeks ago to take temporary charge following the sacking of Ronald Koeman and oversaw three away defeats before Sunday's result.
Baines, scorer of the decisive goal against the Hornets, told evertontv when asked about winning for Unsworth: "It makes it extra special.
"He has been top-drawer. I've loved the training sessions he's put on and the way he has conducted himself. His talk before the game was special.
"We would like to have given him more, and achieved better results – but we have got him a win, which he deserved, at the least."
Ahead of an international break that appears a likely period in which Everton will appoint a permanent boss – be it Unsworth or someone else – it was a remarkable contest that brought the Merseyside outfit's first win since September.
After goals from Richarlison, in the first minute of the second half, and Christian Kabasele put Watford 2-0 up, Everton hit back with efforts by Oumar Niasse and Dominic Calvert-Lewin.
There were subsequently 13 minutes of time added on at the end, during which Baines' penalty completed the turnaround before Watford's ex-Everton midfielder Tom Cleverley missed a spot-kick at the death.
It saw Everton move out of the relegation zone, up from 19th to 15th.
And Baines, who now stands alone as the club's record penalty-scorer on 24, one clear of Unsworth and Trevor Steven, said: "We know we are better than the league table and our performances at times have been showing.
"It was nice to get a win. It was dramatic, so it feels great. But it is nothing to get too carried away with. It is the type of win we should be getting here.
"It's a definite momentum-builder, with the manner of it, the emotional roller coaster. I am sure it was a tough watch."