The offer was made during talks with Sevilla over fullback Daniel Alves as Begiristain seeks to land both players ahead of a host European rivals. In total, Barca are willing to cough up £25 million for the pair.
However, Sevilla president Jose Maria del Nido has knocked back the proposal, informing Begiristain he won't do business over Keita and Alves for less than £33 million.
More talks will continue in the coming days, with Begiristain also discussing the deal with the agents of both Alves and Keita this week.
