The new Everton boss sends his side to Nicosia on Thursday in their final Europa League game of the season with first-team coaches Craig Shakespeare and Duncan Ferguson taking charge as he has not made the trip due to a pre-arranged medical appointment.
Everton cannot qualify from Group E after what has been nothing short of a disastrous European venture this season.
Limassoll have also been eliminated from the Group and they too are set to make a lot of charges to their side but with the Merseyside derby coming at the weekend Allardyce is set to field a weakened team.
Punters may wish to use their free bet to back Everton to get a result in the Merseyside derby, as despite their struggles this season the players will be keen to impress Allardyce and Liverpool also have a midweek European game and still have some work to do to qualify.
Harry Charsley, Nathan Broadhead, Alex Denny, Fraser Hornby and Michael Collins are among the youngsters in contention to be part of the squad and Allardyce could also give an opportunity to summer signings Sandro Ramirez and Davy Klaassen as they look to impress.
Both players were left out of the win over Huddersfield on Saturday and are keen to get an opportunity to show the new manager what they are capable of doing.
With Everton's fate in the group already determined and Sunday's clash with Liverpool to prepare for, assistant manager Sammy Lee has also not made the trip and will work with the players who have not travelled.