Suarez has played only once this season – a 1-0 Copa del Rey victory over minnows Deportivo Leonesa in which manager Ernesto Valverde rotated his entire first team.
And Spanish publication Marca claim Sarri is ready to rescue him from his Nou Camp nightmare.
Sarri was reportedly keen on the midfielder while he was manager of Napoli.
And he might need midfield reinforcements at Stamford Bridge as the long-term future of on-loan Real Madrid midfielder Mateo Kovacic remains uncertain.
Even if Sarri wanted to make the deal permanent, Kovacic has three years left to run on his contract at the Bernanbeu and his release clause is set at a whopping £262million.
Real are unlikely to demand a fee anywhere near that but reports claim they are likely to want close to £50m.
Any deal would also hinge on whoever the next manager is, with Real currently searching for a replacement for Julen Lopetegui who was sacked last month.
Suarez, though, could be available at a knockdown price having fallen spectacularly out of favour under Valverde.
He was a Barca regular in his first season under former boss Luis Enrique, who signed him from Villarreal in the summer of 2016.
The 24-year-old also has experience in England having played for Manchester City at youth level.
While he did not make a single Premier League appearance, Suarez made his City debut in the League Cup in 2011-12 and appeared in the FA Cup the following season.
He has represented Spain at every level youth level and has one full international cap.
Blues boss Sarri is understood to want reinforcements after making just two first-team signings in the summer.
Italian midfielder Jorginho was brought in from Napoli, while Spain keeper Kepa Arrizabalaga joined from Athletic Bilbao.
Sarri has also been linked with an ambitious move for Inter Milan striker Mauro Icardi.
Sarri’s old club, Napoli, are also still interested in Suarez, as are Barca’s La Liga rivals Valencia.