Catalan publication Sport claims that the Spaniard and the Gunners have already "reached an agreement in principle" with the deal expected to be finalised once Sanllehi arranges a final settlement over his exit from the La Liga giants.
Sanllehi has been one of the main figures responsible for the transfers conducted at Barcelona across the last decade.
He joined the Catalans as director of relations with sport bodies and in 2008 was promoted to the role as director of football.
During this time the Spanish chief was especially active in the recruitment of players from South America and he played a crucial role in the major deal that saw Barcelona beat Real Madrid and other European clubs for the signing of Neymar from Santos in 2013.
But some weeks ago it emerged that Sanllehi was ready to leave his post at Barcelona following a hectic and disappointing summer transfer window at the Nou Camp.
Noticeably, the club lost Neymar to Paris Saint-Germain and failed to bring Philippe Coutinho from Liverpool despite being identified as a priority target by manager Ernesto Valverde.
Manchester City and Arsenal have thus been linked with his services in recent times.
It looked that Pep Guardiola's side could have an advantage in a potential race with Sanllehi having previously worked with City chiefs Ferran Soriano and Txiki Begiristain at Barcelona.
However, Sport claims that Sanllehi is instead set to join Arsenal as he also has a close relationship with Gunners chief executive Ivan Gazidis.
The Spanish publication claims that Sanllehi is expected to fill the gap left by Richard Law's departure after the Arsenal transfer negotiator recently decided to step down from his position at the Emirates Stadium.
Law joined Arsenal in the summer of 2009 to cover a job that had been vacant since the departure of former chief executive David Dein in 2007.
He has since been club's principle transfer negotiator and was said to play a major role in the £42m signing of Mesut Ozil from Real Madrid in the final days of the 2013 summer transfer window.
The news about Sanllehi's expected appointment comes only a day before Arsenal hold their Annual General Meeting on Thursday (26 October). Both Arsene Wenger and Ivan Gazidis are expected be grilled by the club shareholders following another quiet summer transfer window at the Emirates Stadium.