The Reds have agreed a €75 million fee with Barcelona over the striker's sale.
Rodgers faces the task of replacing a player who scored 31 goals last season and led Liverpool to the brink of the Premier League title. QPR striker Loic Remy and Swansea's Wilfried Bony are his early targets.
But Rodgers promised: "I am confident we will improve the team further and will be stronger for this coming season. If there is one thing the history of this great club teaches us, it is that Liverpool is bigger than any individual. I hope our supporters continue to dream and believe that we are moving forward and with continued improvement and progression, together we will bring the success we all crave and deserve."
For the big stories and the banter follow us on Twitter: @tribalfootball