It was reported last month that the Catalan giants are prepared to listen to offers for the 27-year-old who has endured a mixed experience since his return to the club nearly three years ago.
Fabregas is on the radar of both Manchester United and Arsenal, where he spent eight highly successful years and finished up as club captain.
The Gunners are understood to have first refusal on the Spain international, whom they sold to the Spanish giants in 2011 but Parlour has urged Wenger to instead target a marquee striker to provide competition for the overburdened Olivier Giroud.
Parlour, whose sale to Middlesbrough in 2004 paved the way for Fabregas to make his mark on the Arsenal first team, told the Daily Mirror: "The problem with Fabregas is where do you put him in the team?
"They have got very similar players to Fabregas – they have Mesut Ozil, Santi Cazorla, Jack Wilshere – if you bring Fabregas back where do you fit him in?
"He was great for the club but forwards should be much more of a priority.
"You look at Manchester City and Liverpool and they have much better forwards."
Giroud was often forced to plough a lone furrow up front for the club last season, as they finished fourth, with Yaya Sanogo and Nicklas Bendtner his only support after bids for Luis Suarez and Gonzalo Higuain came to nothing.