Phillips has been in fine form for the Baggies since Carlos Corberan arrived at The Hawthorns - but could be out for the rest of the season after having surgery on a quad muscle injury.
Neither Grady Diangana nor Karlan Grant have overly impressed for Albion on the left flank, and Corberan wants more options as Albion chase a play-off place.
Hutchinson, 19, has one cap for Jamaica and has played twice for Chelsea's first team - and is on Albion's radar according to reports.
If he moves to the Midlands on Tuesday he will be the second arrival at The Hawthorns after Albion completed a deal to sign Fulham midfielder Nathaniel Chalobah.
The 28-year-old has signed an 18-month deal with Corberan's promotion-chasing team and he told the Express & Star: "I heard about the club's interest in me a little while ago so I'm glad to finally get the deal done.
"Ever since I heard about the interest in me I obviously started following the club's results a lot more. I've been watching plenty of the games recently and from what I've seen, it's been pretty good.
"I definitely see so much potential in this team. I see that there's a talented group of players here and I just want to play a part in everything."
Corberan said: "Chalobah is an athletic, hard-working midfielder who has the quality required to make a real impact in the Championship.
"To do that he will need to consistently play to a high standard and take his opportunity when it arises.
"I believe strongly that competition for places must be intense and recruiting Chalobah to the squad will bring out the best in everyone competing for a position in the team.
"We will work with him closely to ensure he is ready to fight for every point between now and the end of the season."