Struber has reportedly been targeted by the Red Bulls, seeking a new head coach after parting company with Chris Armas earlier this month - with some reports in his native Austria stating he is ready to take on the challenge in the US.
The 42-year-old has a buy-out clause in his Reds deal allowing him to speak to rival clubs if they agree a set figure.
Speaking about his future after Saturday's 0-0 draw with Coventry City, he said: "At the moment I am here as coach and we will see what the future brings. Right now, my focus and concentration is on my boys.
"I am here. I am the head coach here and I have the responsibility. Many people around me and in the media write about interest from other clubs. At the moment, this is not a new one. I have the focus here and this is my job."
Barnsley picked up their first point of the season in Saturday's goalless stalemate, but on the debit side, they have still yet to find the net in the league so far in 2020-21.
The Reds' toils in front of goal at Oakwell have seen them fail to score in seven of their last 11 home league matches - scoring just five times.
That said, their defensive statistics remain impressive with Barnsley having registered six clean sheets in that same number of matches.
Saturday's match again reinforced the club's need to bring in another frontline forward with the strikers who have started at league level for the club having netted just one goal between them in their last 11 Championship matches.
Struber acknowledged: “We can’t score and this is our challenge.
“Some new players can help us and this is the situation at the moment.
“You can see in the last few games that we need reinforcements, especially a new striker.
"We need a big conviction when we have the chance to score goals and this is our big topic. At the moment, we do not find the right balance or smart positions where we can score goals.
"We are in an exchange with some new players who can help us. This is the situation at the moment. You can see we need new players, especially in the offence.
"We had good chances to score goals. It was a difficult game. I expected the opponent in this shape and also with spirit. But it is our first point of the season and 100 per cent not our last."