Pennant is due to play his final game before his loan spell ends, although Peter Reid is hoping to arrange an extension.
It's understood that United have held preliminary talks with the player's agent, but Arsenal boss Arsene Wenger will have the final say.
With The Gunners facing several possible suspensions following their 0-0 draw at Old Trafford last month, it is likely Wenger would want Pennant to return to Highbury.
Pennant has been a revelation to the United side and there is not much alternative on the right flank.
It is known that England U-21 star Pennant would like his two-month loan extended.
Pennant's first-team appearances are limited at Highbury and he feels he will have a much better chance of regular Premiership football if he stays at Leeds.
He has played in all Leeds' Premiership matches since making his debut as a substitute against Tottenham, but Arsenal refused to let him play in the Carling Cup tie against Swindon last month.