The Championship club also have former Bristol City goalkeeper Adriano Basso on trial and Hull's head of football operations Adam Pearson expects to secure a deal for Gulacsi.
"If we're successful in completing the deal, he's a keeper with a lot of potential," Pearson told the Hull Daily Mail regarding the Hungarian.
"Steve Walsh watched him a lot last season at Tranmere and he's very highly thought of at Liverpool.
"There were a number of clubs interested in him so if we get the deal over the line, we'll be delighted.
"We're keen to have another keeper to challenge for the No.1 shirt.
"Adriano Basso is in the box seat. He's here and it's up to him to show he can take the role."