The Toffees are understood to have already reached an agreement of around £44m for a player who failed to score or assist a single goal in the second half of last season.
Allardyce, who was sacked by Everton in May after just six months in charge, has taken a subtle dig at supporters by warning his successor that those inside Goodison Park will not settle for second best.
"Everybody's seen the drop off since Mario Silva (sic) left Watford, or maybe even before then," he told talkSPORT. "I think that he has seen him firsthand and worked with him on a daily basis so he is backing his own judgement.
"What I would say to be careful about though is, if you say you are buying potential, Everton fans do not want potential. They want the absolute first-class player now to play now and to beat and try and rival their big rivals down the road and try and get into Europe.
"If you're buying Richarlison now as a future player, that's not what Everton fans want to see at the moment. They want to see them fighting with the best and up there with the top four."
Richarlison was pictured on Merseyside ahead of undergoing a medical with Everton on Monday morning.