Vlasic, 20, joined the Merseysiders in the dying embers of the summer transfer window for around £10m.
Everton's majority shareholder Farhad Moshiri has reportedly drawn-up a four-name list to replace Ronald Koeman.
Former Toffees defender Michael Ball was "dismayed" by the training incident involving Morgan Schneiderlin and Kevin Mirallas.
Allardyce has reportedly been in talks with Everton's majority shareholder but has moved to quash those suggestions.
Allardyce publicly admitted he would consider succeeding Ronald Koeman at Goodison Park and is seen as the frontrunner for the Everton hotseat.
Gary Cahill, Harry Winks, Harry Kane and Jordan Henderson will all be assessed ahead of England's friendly double-header against Germany and Brazil.
Schneiderlin and Mirallas have endured tough starts to the new campaign and were omitted from the Everton squad that secured Watford win.
Much was made of Everton's recruitment of the Spanish forward, but he has failed to make any sort of impression during his time on Merseyside.
The Everton hierarchy will meet to try and find Ronald Koeman's successor during the international break.
Everton striker has been in the doghouse for being found guilty of drink-driving party girl Laura Simpson home after a Cheshire night out.
Martina suffered a neck problem after landing awkwardly during Everton's loss to Lyon but Unsworth confirmed that the defender did not suffer any serious damage.
Robinson has made seven league appearances for Bolton this season and will remain at the Macron Stadium until at least January.
Martina suffered a heavy fall and required serious medical attention during the first half of side's defeat by Lyon.
Sam Allardyce, Sean Dyche and Marco Sliva have all been linked with the vacant post at Goodison Park.
David Unsworth's beleaguered Toffees face a very tough task against Bruno Genesio's side at the Groupama Stadium.
Burnley's manager Sean Dyche remains among the favourites to take over at Goodison Park as Koeman's replacement.
Feeney has impressed for Everton's youth squads and has trained with the senior team on a few occasions this season.
Santo has elevated Wolves to the top of the Championship table after taking the reins at Molineux in the summer.
Giroud was close to joining Everton in the summer transfer window but eventually decided to remain at Arsenal.
Gray wreaked havoc against Everton on Sunday (29 October) and is determined to build upon his impressive display.
Neville thinks Everton's senior defenders are not helping interim boss David Unsworth, who faced unfair criticism after the Toffees lost to Leicester City.
Burnley manager Sean Dyche has been linked with a move to Goodison Park to replace Ronald Koeman, who was sacked last week.