The Telegraph had said the 26-year-old Scot and Hamilton, who also no longer manages his son Lewis Hamilton, parted "some weeks ago" for unknown reasons.
A spokesman for di Resta, who is linked with a move to Mercedes for 2013 in the event Michael Schumacher returns to retirement, confirmed the split to the Scotsman and Sun newspapers, but did not elaborate on the reasons.
Grenada-born Hamilton, 56, has not commented.
But the Scotsman said di Resta or Hamilton have no plans to formally announce the split.
Martin Brundle, a former grand prix driver turned lead British television commentator, tipped di Resta for a bright future.
"There is no doubt that Paul will be on the shopping list for consideration by several top and well funded teams in the future and he is unquestionably a great talent," he said.
"It's too early to say if he's world champion material."