The Australia all-rounder announced his retirement from Test cricket on Sunday after withdrawing from the ODI series against England through injury.
Watson, 34, previously played for the county in 2004 and 2005.
"He has often said he would like to return if the opportunity comes up," Hampshire director of cricket Giles White told BBC Radio Solent.
"It will depend on his availability more than anything, but initial contact has been made.
"I'm not sure how long things will take, but certainly there's a will there."
If Watson was to rejoin Hampshire next season, White confirmed it would be for white-ball cricket only.
"It's likely to depend on the structure of the competitions and the international fixtures next season, but we'll see how it goes," he added.
Watson played in 59 Test matches, scoring 3,731 runs at an average of 35.19 and taking 75 wickets at 33.68.
He was part of the Hampshire side which won the 2005 C&G Trophy at Lord's. He signed again for the county in 2008 to play in the T20 Cup but had to withdraw because of international commitments.
Hampshire have confirmed they have made contact with Shane Watson about playing for the county next season.