Southampton have stolen a march on their Premier League rivals including Norwich City who were interested in the striker by having a bid accepted for Blackburn front man Adam Armstrong.
Armstrong, 24, is set to have a medical with the Saints on Tuesday after the bid, which could be worth more than £20m with add-ons, was accepted.
He scored 28 goals in 40 Championship games in 2020-21, the second-highest figure in the division last season.
Southampton are in need of a striker after selling 29-year-old England international Danny Ings to Aston Villa for £25m earlier this month.
Armstrong, who represented England at Under-21 level, began his career with Newcastle and had loan spells with Coventry, Barnsley, Bolton and Blackburn before moving to Rovers on a permanent deal in 2018.
Southampton had an offer rejected for Armstrong last week, but returned with an improved bid.
The Saints finished 15th in the Premier League in 2020-21 and begin their 2021-22 campaign away at Everton on Saturday, 14 August.