The Dutchman has seemingly pulled out of Boro's pre-season tour with the paper suggesting a £1m deal is close.
Swansea have long been admirers of the 23 year old, who enjoyed a successful loan spell at the Liberty last season.
They are also thought to be keen on a deal for his fellow Middlesbrough forward Leroy Lita, but so far, bids for both have failed with the club holding firm.
Last week, Swans chairman Huw Jenkins remained optimistic of striking a deal.
"We had initial discussions with Middlesbrough a few weeks back but the figures quoted were a lot different from what we think the values are," he told the South Wales Evening Post.
"Things can change in football, and things could change for Middlesbrough or for us.
"All I would say is that at the moment, Brendan is talking to different people and I am talking to different people to see what is out there."