According to a report by Daily Mail, the 24-year-old has been linked with a number of English sides this summer, but Fulham is expected to secure the Iranian player.
Hajsafi represented Iran at the 2014 FIFA World Cup in Brazil and has more than 60 caps.
He can play at left-back or in midfield and will cost around £250,000, Daily Mail reported.
Fulham was relegated from the Premier League last season for the first time in 13 years.