Pellegrini is leaving Manchester City to be replaced by Pep Guardiola.
Everton parted company with Roberto Martinez last week after a disappointing season from the Blues.
The talk is already fierce about who may replace him at the club, with a number of managers having been linked.
Southampton manager Ronald Koeman is among those, although at present a move for him seems unlikely to say the least.
And Nicholas says that if they are targeting the Dutchman, then departing Manchester City boss Manuel Pellegrini should also be on their list.
“I don’t know what everton are thinking of, but if they’re linked with Ronald Koeman then they should be linked with Manuel Pellegrini,” he told Soccer Saturday.
“They’ve even been linked with Mourinho, so why not get out there and test the market and find out from the top guys if they’re available.”
Pellegrini certainly wouldn’t be a poor choice for Everton given his history of managing big clubs.
He did extremely well with Real Madrid, as has Champions League pedigree, having done well with Malaga and leading Manchester City to the Champions League semi finals this year.
The last two seasons at City have not been the best for though, despite him spending big money at the club, at that could very well play it’s part in Everton’s thinking.