It is believed that Hampshire batsman Vince will come into the setup following James Taylor's recent retirement because of a heart condition.
The right-hander recently impressed against Yorkshire with a knock of 119.
Like Vince, Nottinghamshire's 25-year-old seamer Ball also made the headlines during his outing versus Yorkshire last week as he took seven wickets, including that of England batsman Joe Root.
It is also expected that despite some early poor form with Middlesex, Nick Compton will retain his place in the 13-man selection.
The first Test against the Sri Lankans gets underway on May 19 at Headingley.