He spent two spells on loan with Watford last season and admitted earlier this year that he might have to consider a permanent move to further his career.
Pennant, who had struggled to break into the Arsenal side following his £2m move from Notts County, a record fee for a teenager, five years ago, was sent off for punching Niko Kranjcar in an off-the-ball incident during the U-21s 3-0 friendly defeat at Upton Park last night.
Jermaine Jenas, the Newcastle United and England U-21 midfielder, is convinced that Pennant, who is expected to receive a three-match suspension from U-21 and senior international friendlies, will learn his lesson.
"I saw Jermaine in the changing room after the game and he was very disappointed with his reaction," Jenas said. "He knows he should have shown more discipline in that situation. But he's a great player, he'll learn from it and I'm sure he'll move on."
Leeds had been linked with the player over the summer as Peter Reid attempted to increase his options after several high-profile departures.
Pennant, who will wear the No 11 shirt at Elland Road, will be available for all Premiership games, but cannot play in the Carling Cup, and is due to return to Highbury on 19 October.
Reid said: "You always need quality players and getting Jermaine in will be a big bonus for us."