Zekhnini made an impressive performance for Odd Grenland in their Europa League qualifying match against Borussia Dortmund on Thursday.
The youngster grabbed an assists as his side lost 4-3 to the Bundesliga side.
Norwegian newspaper VG has reported that both Manchester United and Borussia Dortmund are now closely monitoring the youngster.
Reports claim United could make a move for the youngster before the September 1st deadline.
Zekhnini has admitted that his biggest dream would be to play at Old Trafford.
“I don’t know where I will be in five years’ time,” he told Nettavisen.
“I will give my best every day. Manchester United is the biggest dream.”