Police are investigating "offensive" comments about a van and a busy shopping centre in an area where there have been objections to plans for a new Aberdeen FC stadium.
The £50m stadium and training facilities would be at Kingsford, close to the Aberdeen bypass, near Westhill.
BBC Scotland can reveal a comment on an online forum for fans stated: "Get in a van and take one for the team.
"The shopping centre bit will be busy this lunchtime."
Aberdeen FC criticised the comment, and urged those backing the stadium plans to support them properly.
The post, on Friday morning, was removed from a thread about the stadium plans.
Police Scotland said officers were investigating a complaint received on Friday 18 August regarding "offensive comments posted on an online public forum".
Sgt Alun Harries said: "Inquiries are ongoing in relation to this complaint, however I would ask anyone with information they think could assist to contact Police on 101 or Crimestoppers on 0800 555111 if you would prefer to remain anonymous.
"I would like to take this opportunity to remind people of their responsibilities with regard to the law when it comes to posting comments online.
"Do not think that because you are behind a screen you are at liberty to say what you like - any report of racist, offensive or abusive comments made online will be thoroughly investigated and every effort made to bring those responsible to court."
An Aberdeen FC spokesman said the club obviously did not in any way condone such comments, even if not meant seriously, and urged all those in favour of the plans to "show their support in a proper manner".
The No Kingsford Stadium protest group said in a statement: "Online messages such this are totally unacceptable.
"NKS will continue to encourage all parties in this debate to condemn all abusive and threatening behaviour."
Aberdeen FC chairman Stewart Milne warned last week the club faces playing European games in Glasgow or Edinburgh in future.
He was talking at a campaign launch to support the new stadium to replace Pittodrie, which he said will soon not meet the criteria to host Uefa games.
However, objectors have called for the club to look elsewhere. Concerns include traffic and parking issues.
A decision is due to be taken by councillors in October.
A pre-determination hearing will take place on 13 September at Aberdeen Town House.