The transfer has been agreed with the midfielder and his club DC United for the 20-year-old who has been capped 18 times by the USA. Spurs fans have already had the chance to see the speedy Convey in action when he was the star-turn in the Tottenham Tribute Match against United last October.
Glenn hopes that the authorities will grant the left-sided player a return to the Spurs stage.
"Terms and agreement with the club have been dealt with - it is just waiting for a work permit," he reported.
"We see Bobby as somebody who has got a bright future and, if we can get that work permit in, he'll come straight into the team."
Convey started his MLS career straight from High School four seasons ago as the youngest player to be acquired in the history of the league - he is recognised as one of DC United's most valuable players.
"He is only 20-years-old, has already won 18 caps for the USA and they have been high quality international games," added Glenn. So he has got a lot of experience for a young man and I see him as a player who can only get better and better.
"He is somebody who would come in and push himself straight into the team, he has got good potential to work with and a bright future."
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Glenn Hoddle predicts that potential signing Bobby Convey would slot straight into the first team should he succeed with his work permit application.