With Lambert's former Southampton teammate Adam Lallana expected to arrive at Anfield in the next 24 hours, Rodgers is confident that he can build a squad that is capable of challenging for honours next season.
"I think there has been a lot of work that has been done," he told Sky Sports News. "If you look at us as a club, we haven't been resting over the course of the off-season, a lot of great work has gone on.
"We've targeted players, we've signed some and we'll have more signings to come over the course of the pre-season. The idea is by the end of August we'll have the squad together and it will be a really exciting time for us next season."
Liverpool get the new Premier League campaign underway at home to Southampton on August 16.