Vince earned his maiden Test call-up for England last summer but was dropped from the squad ahead of winter tours to Bangladesh and India having only managed to score 212 runs in his seven matches.
Hampshire open their County Championship division one campaign today against Yorkshire at Headingley (11am).
It was at the Leeds ground where Vince scored his last red ball century.
The ton, a showcase of the 26-year-old’s talent, forced an unlikely draw for the Ageas Bowl side last April.
It could be pinpointed as the moment selectors inked the opener’s name onto the Three Lions’ squad list.
And White reckons Vince, who will captain the side in George Bailey’s absence, can start his assault to reclaim his England place at Yorkshire again.
He said: ‘It is important for him to start the season well to push his name back into the England frame.
‘We all know he has the quality to do so and is an excellent player. It is just about performances for him.
‘I, and a lot of other people watching him, felt that he very much looked the part and was on the cusp of getting the really big score but it wasn’t to be.
‘Now it is about scoring the runs for Hampshire and getting a second opportunity.
‘If you look at the strong Australian sides over the years with the (Justin) Langers, the (Stuart) Laws and the (Matthew) Haydens.
It was their second coming when they actually nailed their spots.
‘Hopefully that is the same with James.
‘Langer, Ponting, (Damian) Martyn, Hayden, all those guys had a taste of Test cricket then got taken out.
‘On their second time, they got lots of runs in the Sheffield Shield and became influential players for Australia.
‘That is the challenge ahead of James now.
‘In my opinion he is very capable of being competitive at that level.’
White and Vince have an almost full strength side to pick bar Bailey, who’s getting married, and the injured Reece Topley. The 23-year-old is close to returning.
And White is especially excited to see a frontline bowling attack in division one for the first time since promotion three years ago.
‘I think it is probably the strongest squad but it is about keeping them fit,’ he said.
‘I’m really excited to see Reece Topley and Fidel Edwards bowling together, that will be great.
‘Kyle Abbott will come in as well and if we can get a full bowling unit bowling together and bowling well then I will be pleased.’