Black, Steve Bruce's No 2 at the Stadium of Light, hopes to see Bent complete his move on Tuesday and is optimistic the England international's arrival will persuade other targets to move to the North-East.
Bent, who joined Tottenham for £16.5 million two years ago, was at Sunderland on Monday for a medical.
Speaking on BBC Radio Five Live, Black said: "We're very close. I wouldn't say we're 100 per cent confident we're going to get him and we're hopeful that in the next 24 hours he'll be a Sunderland player.
"His record in the Premier League is outstanding, I think he's scored about 50 goals in 100-odd appearances, a phenomenal return.
"There's a plethora of different things we think he'll bring to Sunderland.
"He's a big name, he's somebody who has proved he's a Premier League striker, and his return in goals per game is exceptional.
"So getting someone like him up here can only be good for us, and if it can encourage one or two others to take the leap we believe we're going in the right direction."
Bent would join England Under-21 striker Fraizer Campbell, who has moved from Manchester United, Albanian midfielder Lorik Cana from Marseille, and Paraguay defender Paulo da Silva as new signings at Sunderland.
The anticipated fee of around £12 million for Bent would eclipse the club-record £9 million spent on Scotland goalkeeper Craig Gordon, who was bought from Hearts in August 2007.
Wigan's Lee Cattermole is another target but the Latics have resisted attempts to prise the former Middlesbrough midfielder away from the DW Stadium
Bruce and Black know Cattermole's strengths, given they were the management team at Wigan until leaving for Sunderland in June.
Black added: "We put offers in to Wigan which have been refused and he's a Wigan player, it's as simple as that.
"We rate him very highly because we had him previously and we think without doubt he could do a job at Sunderland, but he is a Wigan player and that remains the case."