Newly-promoted Premier League club Middlesbrough are interested in signing the 26-year-old Brazilian.
Cardiff drew 0-0 at Birmingham City and Trollope said Fabio's future could be resolved next week.
"Coming into the first game of the season we wanted everyone fully focused on the job in hand," Trollope said.
"The timing wasn't great for us but hopefully there will be a resolution next week.
"There has been an interest from another club and that was the reason he was left out."
Fabio joined Cardiff from Manchester United in January 2014 and has made 64 league appearances for the Bluebirds.
Wales international Declan John was preferred to Fabio at left wing-back against Birmingham at St Andrews.
John, 21, has been handed his chance by Trollope having not featured under previous boss Russell Slade and sent on loan to Barnsley and Chesterfield.
"I think he'll get stronger," Trollope added. "He hasn't played football regularly at this level for a while so I think there's more to come from Dec.
"I've got a belief in him and what he is and what he can bring to the team. I'm delighted to see him out there putting in a good performance."
Cardiff and Birmingham fought out an entertaining goalless opening day stalemate at St Andrews.
Trollope, appointed Cardiff boss in May, was encouraged by his side's performance in his first competitive game in charge.
"We've tried to be really positive in the final third, tried to be brave and take chances when they come," Trollope said.
"The game plan worked to a certain extent. There's always things to improve on and we'll learn from this."
Cardiff defender Fabio Da Silva was left out of their opening game of the season because of interest from another club, manager Paul Trollope has said.