McLeish has identified Wigan winger N'Zogbia as the ideal replacement for Liverpool-bound Stewart Downing and is willing to match Wigan's ?10million valuation.
Third time lucky? Bruce has failed with two previous bids for Charles N'Zogbia (left)
But Bruce has refused to give up the chase on the Frenchman despite having two offers rebuffed by Wigan chairman Dave Whelan in the past 12 months.
The Sunderland boss and chairman Niall Quinn have signed nine new players in the summer but Bruce has yet to fill his problem left-hand side position.
New boy: Craig Gardner
He is now hoping to convince Sunderland owner Ellis Short to make N'Zogbia his 10th, and most expensive addition of the close season, while shedding at least three players from his current squad.
Bruce said: 'If you look at what we have in the squad, I think we have a really good balance now. We have four strikers, six or seven defenders and a host of midfielders as well. We're OK.
'I'm really happy and, if I don't do another thing, I'll be quite happy to go into bat with what we've got. We've got a good balance.
'But if there's one area where we're maybe a little bit short it's a natural wide left player, but there's not many of them about.'
Young midfielder Jack Colback filled the role in Wednesday's 2-1 pre-season friendly win at York, in which only Craig Gardner was the only one of the new signings to appear.
Striker Connor Wickham and South Korea international Ji Dong-Won only join up with the 23-man squad ahead of their visit to a training camp in Germany.
Meticulous planning has gone into Sunderland's pre-season preparations,which include games against Arminia Bielefeld, Hannover 96 and BorussiaMoenchengladbach.
And Bruce, who still has two Premier League loan signings up his sleeve before the closure of the transfer window, is confident this summer's policy of buying early will help his squad hit the ground running when they kick off at Liverpool next month.
He said: 'I always felt it was going to be important to get as many players in as quickly as possible, and Niall agreed. We lost six players so it was important to get a few in before we started. At least it'll give us five or six weeks to work with them.
'The big thingfor me was the two Manchester United boys O'Shea and Brown. I think when they joined there was a real feel-good factor about things and all around the town, everybody's talking about the start of the season and that's terrific.
'To get two established players out of Manchester United is quite a coup. If I'm honest, I didn't really think it would be possible. Two or three years ago, it probably wouldn't have been, but now they're looking at it and seeing that Sunderland are having a right good crack.
'It's up to us now to get a team together with what we've got but we're going in the right direction.
'The eight days in Germany will be vitally important because we'll getall of the new lads away and they'll get to know each other a bit better.'
Among the party travelling to Germany is free signing David Vaughan who admitted it was a wrench to quit Blackpool.
Recruitment drive: Bruce has signed nine players during the summer
But the quietly-spoken Wales international is confident he has made the right move after turning down West Brom and Fulham to join Sunderland.
Vaughan said: 'It's been a little bit stressful this summer leaving Blackpool. I didn't really want to leave but being relegated made my decision for me and the main reason for leaving was to stay in the Premier League.
'Blackpool will always be a special place for me, the promotion was special and some of the results and moments last season as well but it was just tinged with disappointment because of relegation. In a few years I'll look back with fond memories on my time there.
'I've come here to do my best and fight for my place. Being in the Premier League taught me just how difficult it is. You've got to play to your full potential in every game. You've got to be confident you can play in a team like this or it's pointless coming really. If I can get my chance in the team I can show what I can do. '
Bolton join chase for United striker Welbeck as Coyle aims to boost attacking optionsCaption competition: Your chance to win ?100 Sportsbook bet with Paddy PowerCLICK HERE TO SIGN UP FOR OUR FREE FANTASY FOOTBALL GAME