The Herald newspaper, once the mouthpiece of the Mugabe regime, said police were making progress in their probe into Grace’s role in allegedly smuggling ivory to China, the United Arab Emirates and the United States.
“We are closing in with our investigations,” a police source told the paper under the headline “Police tighten noose on Grace Mugabe”.
“We have also picked up and questioned several suspects whom we believe are linked to the case.”
Documents from the Zimbabwe parks authority allegedly accuse Grace Mugabe of ordering officials to grant her permits to export millions of dollars of ivory as gifts to foreign leaders.
Once outside Zimbabwe, the ivory was routed to black markets.
A police spokesman declined to comment to AFP on Friday.
Grace Mugabe had been tipped as a candidate to succeed her husband, 94, who ruled Zimbabwe since independence from British colonial rule in 1980.
But he was forced to step down in November last year following a military takeover that ushered former vice president Emmerson Mnangagwa to power.
Grace has not been seen in public since, but she attended a press meeting her husband held at their house in the capital Harare last month.
She was known for her lavish spending habits and fierce verbal attacks on her husband’s perceived critics.