The SPL champions will now enter the Europa League after losing 2-1 on aggregate following a 1-1 draw in Sweden.
"We will be bringing more players in, of that we are very confident," Whyte told Sky Sports.
"Last season we didn't get players in until the end of August.
"We have been working very hard in terms of transfers and we have recruited three new players and secured others on long-term contracts. We have at least half a dozen offers out there and hopefully we will get a couple this week," he added.
The Blues have already signed Juan Manuel Ortiz, Darin Goian and Lee Wallace over the summer.
The Glasgow club now have a break in the League and will face Chelsea in a friendly at Ibrox on Saturday.