The United States international is set to link up with his new Chelsea FC team-mates in the summer after the Blues agreed a deal to sign the Borussia Dortmund playmaker in the 2019 January transfer window.
Hazard is expected to complete a move to Real Madrid in the coming weeks after reports suggested los Blancos had reached an agreement with Chelsea FC for their prized asset.
If the number 10 departs for Real Madrid as anticipated, Chelsea FC will be lacking genuine creativity and pace in their attack next term.
Pulisic operated as a playmaker in the Borussia Dortmund team, with a modest return of 19 goals in 219 games in all competitions for the German club.
Former Manchester City midfielder Wright-Phillips doesn’t believe too much pressure should be placed on Pulisic ahead of the new season.
“I wouldn’t say Pulisic is there to fill Hazard’s boots,” said Wright-Phillips, speaking exclusively to 888sport.
“It’s not fair to put that load on him. He’s there to bring another way of playing for Chelsea and he will create his own footprints basically and build his own legacy there at the Bridge. He is definitely a player the fans will like.
“In America he is rated very, very highly.”
Chelsea FC finished a difficult first season under Maurizio Sarri on a positive note after the Blues finished in third place in the Premier League table.
The west London side also got their hands on some major silverware when Chelsea FC were 4-1 winners against Arsenal in the Europa League final in Baku last month.
Read the full 888sport interview with Shaun Wright-Philips, including this thoughts on why Chelsea need to start giving managers more time
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