The 33-year-old has again been a vital player for the Yellow Submarine during the 2022-23 campaign, scoring once and providing five assists in 36 appearances in all competitions.
Parejo started his professional career with Real Madrid, but he struggled to make the breakthrough at Bernabeu, ultimately moving to Getafe in 2009, spending two years with the capital outfit.
The Spaniard then joined Valencia and went on to make 383 appearances for Los Che over nine years before ending his association with the club in the summer of 2020.
Parejo has been a key player for Villarreal since his arrival, featuring on 135 occasions in all competitions, contributing seven goals and 26 assists in the process.
According to Mundo Deportivo, Barcelona view the experienced midfielder as a genuine option this summer, with the Catalan club's head coach Xavi determined to boost his options in that area of the field.
Parejo has a contract with Villarreal until the summer of 2024, but the report claims that he could be released at the end of this season to allow him to move to Camp Nou on a free transfer.
Manchester City's Ilkay Gundogan is also said to be a leading target, with Parejo potentially arriving alongside the German, as Sergio Busquets could depart on a free transfer.
Franck Kessie has insisted that he will not be leaving Camp Nou this summer, but there is again speculation surrounding the future of Frenkie de Jong, with Manchester United said to be keen to reignite their interest.
Parejo's vast experience of playing in La Liga is said to have made him an attractive proposition for Barcelona, with the Spaniard featuring on 444 occasions in Spain's top flight.
The midfielder has also played 39 times in the Champions League for Valencia and Villarreal, with Xavi believed to view him as the ideal low-cost acquisition in the summer market.
Parejo has played 24 times in La Liga during the 2022-23 campaign, with Villarreal currently sitting sixth in the table, boasting 37 points from their opening 24 matches.
The midfielder has also played six matches in the Europa Conference League, with the Yellow Submarine biding to reach the quarter-finals at the expense of Anderlecht.
Both Villarreal and Barcelona will be in La Liga action on Sunday, with the former taking on Real Betis, before the latter, who have seen their lead at the summit cut to six points, travel to San Mames to tackle Athletic Bilbao.