The Daily Mail says Eto'o has been linked to both clubs and Barca are aiming to sell the Cameroon international within a week to raise funds to land their other top targets.
Spurs boss Juande Ramos, a long-time admirer of Eto'o, needs to bolster his strikeforce following Robbie Keane's move to Liverpool, while Chelsea manager Luiz Felipe Scolari has last season's top scorer Didier Drogba on the injury list.
Barca director of football Txiki Begiristain told The Sun: "The days are going by and the market is closing.
"If there is a decision on Eto'o, the best thing would be for it to be made before the Champions League qualifiers on August 12. We're in the process of looking at how everyone reacts, above all how the manager is with the group and with the player."