Four buzzard nests and one goshawk nest were found abandoned in Moy Forest at Tomatin late last month.
The adult birds have disappeared and police said some of the sites appeared to have been deliberately disturbed by illegal activity.
Moy Forest is managed by Forestry Enterprise Scotland and the nests were being monitored by its staff.
Insp Mike Middlehurst, a wildlife crime officer at Police Scotland, said: "Raptor persecution is an ongoing issue for the Highlands and we need the public to come forward and work with us to try and eradicate this blight on the Highlands.
"Police Scotland with partners in the Highland Partnership for Action Against Wildlife Crime has worked to increase public confidence in reporting wildlife offences which has resulted in increased reporting.
"In this case a partner agency has a clearly documented history of birds being at this location."
He added: "I appeal to the public to come forward with information which may assist us in detection of wildlife crime which either relates to this incident or any other."
Giles Brockman, environment manager for Forest Enterprise Scotland, said: "I am really disappointed to see this case of deliberate persecution on the National Forest Estate.
"Forest Enterprise Scotland will work closely with partners to stop this unacceptable practice."
Police are investigating the disturbance of bird of prey nests in a forest south of Inverness.