King said: "I have sent a letter to nearly all the clubs to see if we can arrange something at the last minute, but at this stage it's not looking too hopeful.
"I am not looking to play another non league team this weekend, we have had our fair share of opponents from the lower divisions. The only thing I have learnt from these games is the other results."
Swindon had hoped to play Norwich City this weekend after their game against Inter Milan was called off, but this game is now back on, after Inter decided to go ahead with their English tour after the London bombings.
The Elton John concert in June restricted the number of home games that could be played as the pitch needed a month to recover.