The Baggies saw their relegation to the Championship confirmed on Sunday after they were beaten at Arsenal.
It is understood following that loss, Allardyce granted his coaching staff and the players two days off. But they will report back to work tomorrow – with Allardyce set to begin talks on his future after he has taken training.
When Allardyce was appointed boss in December, he signed an 18-month deal at The Hawthorns.
But that contract includes a break clause that –upon relegation – allows either him or the club to terminate the agreement this summer.
It is understood the Baggies are keen for the 66-year-old to remain at the club – with the board having been impressed by the team’s improved performances.
Allardyce has also said in the past he would be open to staying on if he is given funds for a promotion drive.
As it stands, though, there are one or two outstanding issues that need to be resolved.
If Allardyce ends up not staying, the Express & Star understands the Baggies will start a recruitment process that will see a number of potential candidates interviewed.
Those are likely to include former Sheffield United boss Chris Wilder.
Speaking at his post-match press conference following the Arsenal game, Allardyce refused to discuss his future.
He said: “I am not going to answer a question on whether I am staying or going – it will just be a waste of time because I won’t be saying whether I am going or staying.
“It’s too early to consider or talk about. It’s about the disappointment. It’s about having a day or two off and getting ready for Liverpool.
“The most important thing for me and the players is to give everything we have got to try and finish the season with pride in your own performance and your own professionalism.”