The Blues are understood to have verbally agreed to a new five-year deal, worth up to £180,000 a week , with their 18-year-old talent, as lawyers look over the paperwork
A signing date has yet to be agreed between the club and the player but the final arrangements are thought to now be a formality after Hudson-Odoi rejected long-standing interest from Bayern to commit his future to Chelsea.
Wright-Phillips knows what it means to be sought after by two major clubs after moving from Manchester City to Chelsea in 2005.
The former Blues winger is impressed with Hudson-Odoi's early career and believes Eden Hazard's £88 million ($107m) departure to Real Madrid means that the pathway is now open for him in west London.
"For me, I thought he always had to stay," Wright-Phillips told Goal at the finals of the #BetRegret Cup , part of the nation’s largest safer gambling campaign. "Especially with Hazard leaving. It has opened a pathway for him. He can become that person.
"Maybe not to Hazard’s capability, but he has the potential to create a lot of problems for teams in the Premier League. He is an entertainer. He likes to take people on, create chances and score goals. I think, as a fan, when you are sitting there in the stadium you want to be on the edge of your seat.
"He brings that X factor of what will he do next? So, I think he will be good for Chelsea. Sometimes, for me, age doesn't matter if you have the maturity of a man, which is something he has. He has learned and the more games he has played in and around the first team, the more experience he gets.
"I think he has grown into it really well. Now he just needs to keep his consistency level up to show what he is capable of. I love watching both (Ruben) Loftus-Cheek and Callum Hudson-Odoi. I think they are going to have big seasons for Chelsea.
"You have seen them do it at the end of last year and I think now they will do it on the big stage this year."
Chelsea are going to have to discover a way to be creative and score goals in the absence of Hazard after the Belgian superstar scored 21 goals and provided 18 assists last season, and Hudson-Odoi will be part of the formula to replace their departed playmaker.
Christian Pulisic is the only major incoming of the summer in west London, as he was signed before FIFA's transfer ban was implemented on the Blues. The £58m ($70m) signing from Borussia Dortmund has made an impact with two goals in pre-season and he is likely to start against Manchester United for his side's first game of the 2019-20 season on Sunday.
Wright-Phillips hopes that comparisons with Hazard do not put undue pressure on the USMNT international, but he is happy that his old club have attracted a player who he has watched for some time.
"I like the way Pulisic plays," he added. "I have kept an eye on him from when I was in the United States. I watched a lot of Dortmund. I like the way he plays; he drifts in and out of games. Nice touches, takes people on and he knows where the net is as well.
"So, for Chelsea, they have two exciting wingers. They need to get them on the ball as much as possible. I don’t think you should compare either of them to Hazard. He was in a league of his own when he was there. I feel like they have just got to show the world what they are capable of."
Wright-Phillips was speaking from the final of the #BetRegret Cup, part of the UK’s largest safer gambling campaign . Teams from across the UK have been battling it out throughout the summer, which culminated at the national final at Powerleague Shoreditch on August 4. Bet Regret is that immediate sinking feeling you get when you place a bet you know you shouldn’t have, for example when you’re bored, drunk or chasing losses.