The 19-year-old midfielder was one of the very few bright spots in a disappointing Southampton side that got relegated from the Premier League last season.
He is almost certain to leave the Saints this summer with Chelsea, Arsenal and Manchester United believed to be interested in signing him this summer
Chelsea and Manchester United have held talks with the player’s camp but Arsenal are set to go one step further in their pursuit of Lavia.
It has been claimed that the Gunners are preparing to put in an opening bid for the Southampton midfielder.
Mikel Arteta likes the youngster and believes he has a high ceiling, which he can achieve at the Emirates.
It is unclear how much Arsenal are likely to offer as their opening salvo but Southampton do not want to sell him at a cut-price fee.
Manchester City have a £40m buyback option on Lavia but that only comes into effect next season.
Southampton are looking to get somewhere around £50m before they are willing to sanction his sale this summer.