The Gunners have been linked with a sensational swoop for the Barca midfielder, with Arsene Wenger reportedly keen to bring the Spaniard back to the club he left in 2011.
Widepsread reports have linked the North London outfit with a £30 million bid for the Spain international, but Parlour feels that a move for the attacking midfielder should not be high on the priority list this summer.
Parlour, who spent 12 years at the club, thinks that a striker is more of a pressing concern for Wenger when the transfer window opens.
The 41-year-old, who was nicknamed the Romford Pele during his time with the Gunners, feels that Fabregas is too similar to a number of players in the current squad.
Parlour is quoted as saying to The Mirror: “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.”
Despite the Gunners' interest, Manchester United are also thought to be keen on Fabregas, with new boss Louis van Gaal set to be handed a huge warchest to return the Red Devils to the summit of the English game.
The 27-year-old will be part of the Spain squad that heads to the World Cup looking to retain the trophy they won in South Africa in 2010.
Fabregas made his Arsenal debut 11 years ago and won the 2005 FA Cup before going on to take the captaincy in 2008, and he only added fuel to the fire when he was pictured leaving a London restaurant with his partner earlier this week.
Meanwhile reported Arsenal target Loic Remy showed that he can dovetail with Gunners striker Olivier Giroud as they were both on the scoresheet in France's 4-0 win against Norway on Tuesday evening.
Giroud netted twice before QPR forward Remy, who is said to be attracting the interest of the North Londoners, added a third on 67 minutes, after Paul Pogba had opened the scoring.