Along with sporting director Joe Savage, he is scouring the free agent market for a keeper able to compete with first-choice Craig Gordon and deputy Ross Stewart.
Hearts made eight signings to strengthen their squad after returning to the Premiership and are unbeaten in their first seven league games this season.
Another goalkeeper would take that figure to nine but Neilson has yet to find a suitable candidate. He told the Evening News that he is content to wait rather than add another new recruit in haste.
In the meantime, 17-year-old keeper Liam McFarlane is training as third in line behind Gordon and Stewart.
“It's a position we are looking at but there isn't much out there. It needs to be a free agent, someone who can come in and compete,” explained Neilson. “Every signing we brought in during the summer window improved the squad so it would need to be a decent one if we do sign somebody.
“We aren’t just going to take somebody for the sake of it. We do have a couple of young goalkeepers who are progressing as well.
“Harry Stone is out on loan [at Partick Thistle] and that was one of the reasons we wanted to get another keeper in. We also have young Liam McFarlane, who has been doing really well. He has come in and done some training and we will see how he goes.”