The island's council has launched a consultation in a bid to cut down on illegal camps.
The proposals include opening a permanent residential site in the Menai Bridge area as well as two temporary stopping places in the centre of the island and in the Holyhead area.
Residents and businesses are being asked for their views.
All councils in Wales are legally required to provide accommodation for Gypsy and traveller communities.
The shortlist of potential sites includes locating a permanent camp at the existing illegal site in a lay-by off the A5025 between Menai Bridge and Pentraeth.
Other possible sites for the camp would be at a smallholding in Gaerwen or on land at Penhesgyn, near Penmynydd.
The council is also asking for views on a temporary stopping place at one of two potential sites at Mona Industrial Estate and one in the north of the island, to be located either at vacant land on Penrhos Industrial Estate in Holyhead, land immediately to the east of B&M (formerly Homebase), or land to the south of Alpoco.
Anglesey chief executive, Dr Gwynne Jones, said: "We're committed to ensuring that this important month-long public consultation gives all interested parties a chance to have their say.
"Feedback from residents and communities around the proposed sites will be vital in helping us reach an informed final decision."
Public drop-in sessions have been arranged in communities where sites are being considered.
The consultation ends on 11 March.
Three sites have been suggested as possible locations for a permanent Gypsy and traveller site on Anglesey.