Robinson scored 23 goals in 73 appearances on loan at Hereford and Southend in the last two seasons.
The Shrimpers and League One rivals Brighton were both known to be keen to sign Robinson, who would be Swindon's third signing of the summer, following the arrivals of Gordon Greer and David Lucas.
He would join Simon Cox, Billy Paynter and Lee Peacock as striking options for manager Danny Wilson, who may still be looking to add another forward to his squad, particularly if Cox leaves the County Ground.
Several Premier League and Championship clubs are tracking Swindon's player of the year after his 32 goals last season, with the club putting a £2.5m price tag on him.
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