Hampshire have made 28-day approaches to Mark Stoneman, Varun Chopra and Olly Stone, reports BBC Radio Solent.
Openers Stoneman (Durham) and Chopra (Warwickshire) and injured Northants paceman Stone are all out of contract at the end of the season.
But they face competition for Chopra, who has also been approached about a return to his former county Essex.
Stoneman is understood to interest a number of sides, including fellow Division One strugglers Surrey.
The 29-year-old, Durham's limited-overs captain, has been offered a new contract at Chester-le-Street.
But former Bears skipper Chopra, 29 has already intimated to the Warwickshire hierarchy that he would like to return home to the south-east.
He was then replaced by Ian Bell before the start of this season
Stone, 22, is expected to miss the rest of the season after damaging an anterior cruciate ligament while celebrating the wicket of Worcestershire and England all-rounder Moeen Ali in the T20 Blast on 3 June.