Hume's previous contract expired at the end of June, and the young full-back remains in talks with the club.
Johnson revealed that the 22-year-old is still recovering from the hamstring injury picked up in the first leg of the play-off semi final at Lincoln City, and the youngster is continuing his recovery at the club.
Though the two parties have been apart in negotiations so far, the Black Cats head coach believes there is a willingness from all to get a deal over the line.
"At the moment the state of play is just that there is no agreement in place," he said.
"I think there's a will there at both ends, but at the same time there is a bit of a gap.
"He's not quite on the open market because we are able to get compensation, but effectively he is open to offers.
"It's been a bit of a sticky one either way, but we are hopeful of a resolution either way relatively shortly.
"Denver is still injured after his hamstring operation, but he's getting treatment with us so he is still in our building, if you like," Johnson added.
"I'm sure it's frustrating for him at times, but all you can do at these times as a coach or a technical director or a club, is be be open and honest with a player.
"We don't always agree, but at the same time I think both parties respect the openness and the honesty."
Tyrese Dyce has been training with the Black Cats senior group this week, and played during the first half of the 2-0 win over Tynecastle.
Lynden Gooch played the second half at left back with Sunderland s options in that position on both flanks clearly sparse as it stands.
Carl Winchester played the first half at Tynecastle at right-back, before being placed in the latter stages of the second half by U23 player Kenton Richardson.
Johnson says that even if Hume extends his stay at the club, he will look to recruit another option.
"We need another left-back anyway, no matter what happens with Denver - you always want two for every position," he said.