The winger will now head to Merseyside for a medical and to finalise personal terms after the two clubs agreed a fee.
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The 24-year-old has spent his entire career in the Netherlands, beginning at FC Omniworld before moving on to De Graafschap and then Heerenveen in 2009.
In almost three seasons at the Abe Lenstra Stadium, Assaidi made 84 appearances, scoring 20 goals.
Liverpool are also thought to be close to the signing of Nuri Sahin, who is expected to join the Anfield club rather than Arsenal.
Brendan Rodgers also revealed on Thursday that Daniel Agger wishes to remain on Merseyside despite interest from Manchester City as he looks to break the reds back into Champions League contention.