The 26-year-old Dane, released from Turkish club Kasimpasa this summer, has been with the club on their tour of Scotland and has started three games in pre-season for the Canaries.
Bryan Gunn is now awaiting an answer from Askou, who has returned to Denmark to sort out personal business.
"We were impressed with what we saw with Jens from his time with us," he told the Norwich Evening News. "I would expect him to have other offers, but certainly I am hopeful because he has come in and he has integrated with the squad in Scotland and impressed the other players in the squad and it looked like he enjoyed his time here.
"If it wasn't for a personal problem that he needed to go back to sort out he could have still been with us now and we would have been having more personal discussions.
"Unfortunately it's at the end of a telephone at the moment, but he's certainly one that we were keen to make happen if everything is right for Jens as well."