The Eredivisie club have been open to selling Klich, even though they only bought him up last summer from German side Kaiserslautern for a small fee.
According to De Telegraaf, the Poland international has been linked with a move to West Yorkshire.
De Telegraaf report that Twente have now agreed a deal with United, and the 27-year-old will sign once all the ‘formalities’ have been completed.
The usually reliable Dutch newspaper say Klich is yet to undergo a medical but rumours suggest he is flying into Leeds today.
Klich will be the first major signing for Leeds United this summer under new head coach Thomas Christiansen.
Klich had been linked to Leeds even before Christiansen arrived, but since the coaching appointment the Whites have upped their efforts to seal a deal.