The 22-year-old's agent last week moved to deny that talks had taken place over a potential return to Barca, or a switch to Serie A title-chasers Napoli.
Robert claims the European champions were rebuffed in their efforts to sign the midfielder during the most recent transfer window but says he remains an option before next season.
"He's a player we value. We looked at signing him in the winter market but circumstances meant we couldn't do it. Villarreal's stance was logical," he told TVE.
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"It's possible he could come in the summer window. He's a player that Barca could sign."
Robert went on to admit that Barca had attempted to secure a loan deal - with an option to buy - for Celta Vigo winner Nolito, but were ultimately unsuccessful.
"The situation in the last window wasn't favourable," he said. "Celta didn't want it. A loan with an option to buy? Yes, but in the end it couldn't be done."