The striker's loan is due to end in January but he has been a hit in Scotland and has scored two goals in 11 games since arriving in August.
Dundee boss Barry Smith wants to keep Nish, who has helped in his rock-bottom SPL outfit's recent revival, and hopes new Hartlepool manager John Hughes will soon answer.
Smith said in the Daily Record: "We've made contact with Hartlepool about Colin.
"We want to keep him and he wants to be here, which is important.
"We would like him to stay longer, as he's been doing well, but we'll just need to wait and see.
"John Hughes has only been in the job for a matter of days so we have to wait for them to get back to us."