The Reds boss expects the London duo to make more additions to their squads before the deadline with several moves seemingly bubbling under the surface.
The Gunners have snapped up Gervinho from Lille and Charlton rookie Carl Jenkinson but much of Arsene Wenger's focus has seemingly been on keeping hold of Cesc Fabregas and Samir Nasri. Chelsea have only introduced Thibaut Courtois to their squad and are loaning him straight out.
"I expected more buying," he told Inside United. "Especially the likes of Arsenal. I thought they'd have bought a few players.
"But it's early days - 31 August is a long way off and a lot can happen. Chelsea haven't really been busy except with the manager, who will need time to adjust the squad he's got.
"City have bought Gael Clichy and look as though they're signing a few more [Sergio Aguero has since joined]. We expect a big challenge from those two.
"Liverpool have bought a few players, but the important thing is to look at ourselves. We're experienced and have the players to go the distance in all the competitions."
However, the champions face a tough opening to the defence of the Barclays Premier League crown with a particularly difficult start at home.
"The start looks one of the more difficult ones for us," he added. "Chelsea, Arsenal, Tottenham and Liverpool all early on. If we take each one on an individual basis, then we can handle it.