Willian and Pedro have been important players for Chelsea in recent years.
Pedro, 31, was a £19m acquisition from Barcelona in 2015.
Willian, meanwhile, was snared from Anzhi Makhachkala for £30m two years earlier.
Honigstein is adamant they will be goners soon though.
Maurizio Sarri could axe Pedro and Willian (Image: GETTY)
Honigstein told the 5 Live Football Daily podcast: “I think that Willian and Pedro, if they weren’t worried already, probably know that the writing is on the wall, that they will be phased out.
“Chelsea had a big need in those positions. Christian Pulisic can play in any of them, he can also play centrally.
“I think it was a no-brainer as far as getting a guy with his quality in.
“The fact that they chose him I think has a lot of insight into what Sarri is thinking because they wanted him to start with Sarri in the summer so he’s very much a player we have to assume that Sarri wants.
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Pedro could leave Chelsea in the summer (Image: GETTY)
“I think also he suits Chelsea’s game which is also a bit slower under Sarri, a little bit more deliberate.
“I think in a possession team, as he’s shown in the past, he can be very, very effective.
“I don’t think it reflects in any way on Hazard’s future but it probably tells you that Chelsea are willing and ready to upgrade the existing attacking midfielders, which they have to.”
Chelsea could complete more business this month.
Christian Pulisic has been snapped up by Chelsea (Image: GETTY)
A new striker is high on Sarri’s wish list.
He already has two experienced forwards on his books.
However, Alvaro Morata has struggled and Olivier Giroud’s better days are behind him.
The Italian chief has been linked with Bournemouth forward Callum Wilson, Inter Milan star Mauro Icardi and Juventus ace Gonzalo Higuain who is on loan at AC Milan.