"It's a great honour for Devin," Mutiny President Bill Manning said.
"He impressed them and they're picking up the tab for his visit. We expect him to return to Tampa at the end of January."
MLS deputy commissioner Ivan Gazidis said on Thursday that nothing should be inferred from Tottenham paying the way for Barclay's return.
He added: "Tottenham are not looking at him for anything imminent. It's not uncommon for some European clubs to pay to bring in talented young players.
"If they wanted him in reserve matches, that would require the execution of a loan agreement.
"For loans into England, their FA wants a minimum of three months. I certainly wouldn't object to pursuing that, but it hasn't been discussed."
Tampa Bay manager Perry van der Beck helped arrange Barclay's initial training stint in north London after playing alongside assistant boss John Gorman with the Tampa Bay Rowdies.