The Dutchman enjoyed a strong campaign for the Eredivisie side, playing a key role in their run to the Europa League final.
His performances, especially his 20 goals in the league, have caught the eye of several clubs across Europe, including Everton.
The Blues have held a longstanding interest in the midfielder and it now appears that they are close to securing his signature ahead of the chasing pack.
They report that Ronald Koeman’s team are close to making him their first signing of the summer transfer window in a deal that will cost €30 million, around £26 million.
That is a price the Everton boss is willing to pay as he looks to improve his squad for the upcoming campaign.
This morning TuttoMercatoWeb, via the Express, say the Blues have offered £19m, which is £3m short of the £22m price-tag Ajax have put on him, but an agreement is expected soon nevertheless.
Adding goals from sources other than Romelu Lukaku is a top priority and that is something that Klaassen would certainly bring.
Klaassen himself is thought to be excited at the prospect of playing in the Premier League, something he considers a dream move. The chance to vastly improve his wage packet will also be a major incentive.