Sky Sports revealed last week that the midfielder was the subject of a failed bid from Middlesbrough.
Clayton has also attracted interest from Brighton in the recent past, with a £1.5million bid knocked back in January.
The 25-year-old’s future is expected to continue being called into question as the summer progresses, with the former Leeds man having proved himself to be a high-quality Championship performer.
Huddersfield are, however, unfazed by the rumours and expect Clayton to continue filling an important role in their pre-season preparations.
Robins told the Huddersfield Examiner from a training base in Portugal: “There is plenty of speculation at the moment, and not just about our players.
“That’s not something we can influence, all we can do is carry on as usual, and that’s what Adam is doing.
“He has knuckled down, as have all the group, and I am pleased with the way things have gone so far.
“The weather out here is good, the facilities are excellent, and we are working hard.
“We trained after arriving on Sunday and we had two hard sessions yesterday.
“It’s back to it tomorrow, and we will be working hard again as we build towards Saturday’s game against SC Portimonense.”