The boss confirmed there has been no interest in the pair yet, despite them helping Town to promotion from League Two.
Shrewsbury finished second in Mellon’s first season in charge as Woods and Goldson excelled and the boss insisted he is looking to keep the duo.
“We haven’t had any interest in either of them. We had a bit of interest in Woods in January but that wasn’t a deal that appealed to anyone,” he told the Shropshire Star.
“Both these lads love their football and they both understand that they need to play. They don’t want to be moving on and finding themselves on the bench every week.
“Now the season is finished my aim is very much to improve the team I have already got. I am working hard to build a team not dismantle one.”
And Mellon believes Greenhous Meadow is the best place for midfielder Woods and defender Goldson, although admitted Shrewsbury could sell if it was the right deal.
“In the world of football, if a bid comes in that suits all parties then you have to consider it – that’s the way football works,” he said.
“But we haven’t heard anything from anyone, so they are very much part of my plans for next season unless I hear any different.
“Every player wants to play at the highest level possible but it’s about moving at the right time and we won’t sell unless it benefits Shrewsbury.
“The challenge for them now is to make the step up to League One. It will help their development coming up against better players every week.”