The 24-year-old former Rovers striker joined Blues on Monday from Olympiacos on a season-long loan deal with a view to a permanent move.
McLeish made clear his disappointment with his side's performance in their Premier League opener at Sunderland last weekend despite fighting back to force a 2-2 draw - and he could be tempted to throw Derbyshire straight into the mix.
"Matt's in contention for the weekend," the Blues boss told the club's official website. "He's fit enough and he's played a couple of Europa League games and he's ready to go in."
McLeish revealed he had been tempted by a move for Derbyshire, who left Rovers 18 months ago to head to Greece, last summer but brought in Christian Benitez instead.
He continued: "I'm very glad to have acquired Matt Derbyshire. When we went for Chucho, Matt was a player who was run by me at the time but we'd already committed to Chucho, so I just missed out on him.
"When he left Blackburn two years ago he took on a big challenge by going to a foreign country, especially Greece where the weather is extremely hot and the fans are really volatile.
"The passion between Panathanikos and Olympiacos is quite unbelievable, but he's gone there and won trophies and scored goals.
"I think he's a decent finisher and, if we can get the service to Matt, he can score goals because that's his main strength."
Derbyshire would love to make his debut against the club he joined as 17-year-old and is pleased to be back in the Premier League.
He told Sky Sports News: "It would be very nice but right now it's more important to get back on the training field. It's a new start back in England. I'm looking forward to the challenge at Birmingham."
Derbyshire is Birmingham's second forward signing of the summer after the capture of 6ft 8in Serbia international Nikola Zigic from Valencia and the pair join Cameron Jerome, Garry O'Connor, James McFadden and the injured Kevin Phillips on the Blues' books.
"There's a lot of competition up front and that's a good thing," added Derbyshire. "It's up to us to give the manager a headache."
And the former England Under-21 player already has his sights set on earning a permanent deal at St Andrew's, although he has no regrets about his move to Greece, which brought 12 goals in 21 appearances.
"Of course I would (want to sign permanently)," he said. "They're a great set of guys and a great manager.
"I've become a better player during my time in Greece and it's been a great experience that I'd never change."