According to NBC News, Zimmerman and his legal team (headed by Irish American attorney Mark O'Mara) believe they are entitled to the refund because Zimmerman was acquitted of second-degree murder on July 13 for having shot and killed Martin, 17.
The motion to be filed by O'Mara would seek refunds for the money the defense spent on fees for expert witnesses and court reporters for depositions, travel and other similar expenses.
The request is expected to be between $200,000 and $300,000 according to Shawn Vincent, a spokesman for Zimmerman's legal team who spoke to NBC. Vincent said attorney fees for the defense team, including O'Mara, wouldn't be part of the motion.
The state Judicial Administrative Commission, which would be responsible for paying out the money if the request is approved, didn't return a call from NBC seeking comment.
Zimmerman's request was first reported by The Orlando Sentinel, which quoted O'Mara as saying he would soon file the motion with state Circuit Judge Debra Nelson.
Zimmerman's request to have his costs paid is based on a Florida law that says a defendant who's acquitted isn't liable for costs associated with his or her case. It must be approved by a judge or a clerk.
But O'Mara told the Sentinel he expects the Judicial Administrative Commission to fight the request. 'That's where the fight is,' O'Mara said, adding that he's been paid nothing by Zimmerman but has kept all billing records.
Zimmerman, 29, was acquitted last month of all charges including second-degree murder in the shooting of 17-year-old Martin in Sanford, Florida last year.
Critics have suggested that O'Mara took the Zimmerman case for free, agreeing to defend one of the most reviled men in America, in the hope of cashing in later with a lucrative book deal. It's a claim that O'Mara strongly denies.
'I can't deny the fact that everyone out there seems to think this is going to have future benefits for me,' he said in May. 'I'll deal with it when it comes, if it comes.'