Graham Potter’s side are set to lose a star player in the shape of White, who is in line to complete a £50m move to Premier League rivals Arsenal soon.
With White on his way out, the Seagulls are said to have identified Liverpool central defender Phillips as a potential replacement for the England international.
However, Brighton are in no rush to bring in a replacement for White despite being heavily associated with a move for the Bolton-born central defender.
Potter and his coaching staff are focused on reviewing the existing options in the Brighton squad, with Leo Ostigard, Shane Duffy, Joel Veltman and Dan Burn looking to impress the manager.
Should the English tactician deem the current options at his disposal as not good enough, Brighton could decide to pursue their interest in Phillips or other targets.
Phillips, though, is not short of suitors, with Burnley, Newcastle United, West Ham and Bayer Leverkusen interested in acquiring his services this summer.
Liverpool are said to be ready to sell the 24-year-old if they receive an acceptable bid and have slapped a £15m price tag on him.