The Argentine is back in action after treatment for testicular cancer.
He has figured in a number of reserve games for the Magpies, including a 90-minute run-out in a 1-1 draw with Bolton Wanderers.
The Chronicle claims that Wednesday had scouts at that fixture to cast an eye over Gutierrez.
He is due to be out of contract in the summer and is eager to catch the eye before dropping into the free agent pool.
The Owls can offer him regular outings in the Championship as they push for a top-six finish in the second-tier.
Gutierrez spent time on loan at Norwich City last season, as they suffered relegation out of the Premier League, and could head out of St James’ Park on a similar agreement if Wednesday make an approach.
Stuart Gray has expressed a desire in The Star to get fresh faces onto his books as quickly as possible and Gutierrez would bring top-level and international experience to Hillsborough.