Both fires were on Roockery Park, which is grass land off Mapplewells Road, Sutton.
Three crews including two from Ashfield Fire Station and on from Alfreton attended the grass and undergrowth fire at 8.40pm, April 8 and 5.50pm, April 9.
The fire on April 8 covered about four acres.
Nottinghamshire Police are now instigating the fires.
A police spokeswoman said: "We have received reports of two fires in Sutton this week.
"No one was hurt in the fires – however, we are investigating to establish whether they were deliberately started. If you have any information, please call 101 and quote incident number 627 of 9 April."