The 23-year-old centre-back could be the first player to move between the two clubs since they entered into a strategic partnership last week.
Teixeira, 23, originally joined Stoke from Slovakian side Dukla Banska Bystrica in June 2014 but has since struggled to establish himself at the Britannia Stadium, featuring just twice for Mark Hughes’ men after missing most of his first campaign in England with a broken foot.
The Brazilian-born centre-back, who represented Slovakia at Under-21 level, spent the first half of this past season on loan at League One’s Fleetwood Town and could now make a move to MLS this summer.
Orlando president and founder Phil Rawlins is a former Stoke shareholder and the two teams announced last Friday that they had entered into a strategic partnership, allowing for possible player transfer and loans.
Teixeira has the chance to be the first to make the switch across the Atlantic and travelled out to Florida this week to train with Adrian Heath's side alongside the likes of Kaka and former Potters winger Brek Shea with a view to a permanent move.
On Wednesday, Orlando Sentinel reporter Alicia Rose DelGallo tweeted: "Brazilian defender Dionatan Teixeira (on loan, Stoke City) worked out with Orlando City today as trialist."
After narrowly missing out on the playoffs in their inaugural MLS season, Orlando currently sit seventh in the Eastern Conference 10 games into their second campaign, having recorded two wins, five draws and suffered three defeats to leave them with 11 points.
The club are in desperate need of depth at centre-back after trading Aurelien Collin to the New York Red Bulls last month, and it looks like the 6ft 4in Teixeira could be the answer to their problems.