The Brazilian youngster only moved to Lyon in January from Athletico Paranaense, turning down a bigger offer from Atletico Madrid in the process.
AS says Guimaraes' progress in France has only reconfirmed the opinion of Barca's scouts and the recommendation has been made they move for the youngster this summer.
OL paid €20m for Guimaraes, with the deal including a 20 per cent sell-on clause for Athletico. The player's contract doesn't carry a buyout clause.
Lyon sports chief Juninho Pernambucano recently said of his countryman: "Bruno is a midfielder who is ahead of the play, who has an early reading of what is going to happen around him. A player with a privileged field vision and great technical quality in the pass that fits perfectly into modern football, where you need to break lines and work in tight spaces.
"Every team needs a player like him ahead of the defence. We expected a lot from him, but nobody imagined that his adaptation would be so fast and that he would do the games he did against Juve, Metz and Saint Etienne, for example."