Tigers manager Nigel Pearson told BBC Radio Humberside: "It would be good to [extend Guzan's loan deal] as he's been a real positive for us.
"He's been very positive since he's been here, and I'm very pleased with his contribution."
The United States international was signed as a replacement for fellow loanee Vito Mannone, who returned to parent club Arsenal with a thigh injury.
Mannone, an Italy Under-21 international, has since returned to the KC Stadium and is close to regaining full fitness.
Pearson said of Mannone's ongoing recovery: "He's progressing very well and is doing his rehab with us which he's doing very, very well with. He's probably two to three weeks away."
Source: BBC Sport
Source: BBC Sport