Brazilian team medical chief Jose Luiz Runco said that the players' injuries are "improving well and in the time predicted". "In Kaka's case, there is nothing which is worrying us," he added.
Real Madrid star Kaka has been carrying a left thigh injury for two months, a problem which has dogged his progress in Spain after arriving from AC Milan last summer for 65 million euros. Fabiano has been suffering from a left leg injury and was out of action on a regular basis last season, playing just 23 league games for Sevilla.
Despite his poor appearance record, the 29-year-old Fabiano still scored 15 goals. "They will train with the rest of the squad next week.... their injuries are progressing favourably," said Runco.
Work gets started
Meanwhile, Brazil's World Cup squad began training on Friday amid a crush of excited supporters and reporters. Seventeen of the players converged on a training centre in the southern Brazilian city of Curitiba, out of sight of camera lenses.
The other six from the 23-strong squad were absent for various reasons. Those not present included goalkeeper Julio Cesar, right-back Maicon and centre-back Lucio, who are all due to play for Inter Milan in the final of the Champion League against Bayern Munich in Madrid on Saturday.
Coach Dunga, who turned up late because of flight delays, and the Brazilian Football Confederation had banned media contact with the players to keep them concentrating on their game.
Brazil, five-time world champions, are among the favourites going into this year's tournament in South Africa, which starts on June 11. The Selecao have been drawn in Group G with North Korea, Ivory Coast and Portugal.