Swindon returned to the third tier of the football league after winning the League Two title last season and 27-year-old McEveley believes the Seagulls will provide stern opposition.
"They've got some great individuals and (manager) Gus Poyet has got them playing well. I'm sure they'll be challenging for promotion this season I think that's what they're aiming for so it will be good to test ourselves against them," he told the club's official website.
"The lads last year did well against the likes of Huddersfield and Wigan so we'll go in with a game plan and try to execute it."
Meanwhile, Leicester manager Pearson has admitted he isn't yet sure of his starting line-up as his team travel to Torquay.
"The players have all worked exceptionally hard in pre-season and, for the most part, they've put themselves into a situation where it's going to be a tough choice," he told the club's official website.
Bristol City have striker problems as they prepare to host Gillingham at Ashton Gate.
"Ryan Taylor picked up a knock in training when going over on his ankle and is a doubt for Tuesday," said Robins manager Derek McInnes.
"I only have two senior strikers fit for the game on Tuesday and that obviously leaves us a bit short."
Millwall could hand a start to central defender Danny Shittu when they host League One newcomers Crawley at The Den. The experienced defender, 31, has signed a short-term deal as both Paul Robinson and Tamika Mkandawire are likely to miss the start of the season through injury.
Cardiff will be without Kim Bo-Kyung for their fixture at Northampton. The winger, who played for South Korea at the Olympics, has returned home whilst the club complete their work permit application for the player.
New signings Heidar Helguson, Etien Velikonja and Craig Bellamy will all be vying for a starting position as will fellow new recruit Jordan Mutch who played in the club's 4-1 friendly victory over Newcastle after recovering from a hip injury.
Stephen Carr is a doubt for Birmingham's tie against Barnet at St Andrew's. The full back was withdrawn in the early stages of the club's 3-1 friendly defeat to Royal Antwerp although it is not thought to be a serious injury.
The Blues will also be without young goalkeeper Jack Butland who looks set to make his senior debut for the England national side against Italy on Wednesday.
New signings Hayden Mullins, Peter Lovenkrands, Darren Ambrose, Ravel Morrison and Ben Gordon will all be hoping to make their debuts in the game.
The rest of the fixtures in the Capital One Cup are; Charlton v Leyton Orient, Chesterfield v Tranmere, Dagenham & Redbridge v Coventry, Derby v Scunthorpe, Exeter v Crystal Palace, Ipswich v Bristol Rovers, Oxford v Bournemouth, Peterborough v Southend, Plymouth v Portsmouth, Port Vale v Burnley, Stevenage v Wimbledon and Yeovil v Colchester.