The suspicious blazes have resulted in the destruction of more than 200 bales of hay, with the value of the damage estimated to be more than £5000.
Officers are now visiting local farmers to offer crime prevention advice. They are also appealing for anyone with information to come forward.
A police spokesman said: “Officers are currently investigating whether these incidents are linked and are eager to hear from anyone with information that can help identify those responsible. These fires not only had the potential to endanger lives of the suspects and anyone in the immediate areas, but they have had a significant financial impact upon the farmers.”
Farmers have been warned to look out for suspicious movement around their fields, and they are looking at starting a “Farm Watch” scheme.
John Picken, NFUS vice president, said: “There is an overall crime wave in rural areas which is extremely worrying for all those who live and work in our countryside.
“As well as the additional costs and huge inconvenience of losing and having to replace valuable equipment, fuel or livestock, or in these most recent instances, straw and hay bales, there is also the emotional upset of knowing that criminals have targeted your property.
“Farmers are increasingly vigilant about taking measures that will deter thieves and vandals. It is worth all farmers considering the measures they can take to protect their property.
“The good news is that crime prevention officers are available to give advice to farmers. Many regional staff and local secretaries are now involved in setting up and promoting local Farm Watch schemes.”
He added: “Given that many incidents tend to involve transportation, the police also urge farmers and members of the public to take note of the registration of any suspicious vehicles.
Anyone with any information about the fires should contact police on 0131-311 3131 or Crimestoppers on 0800 555 111.