The North East side were keen on the out-of-favour winger in last month's transfer window and have since been looking to get a deal done in the current loan window, having been unable to in January.
However, the Swans are desperate to remain in the Premier League and have consequently told Boro to take their interest elsewhere, despite them suggesting to the club in the past that they could be able to strike a deal for Montero.
Out-of-favour, but not out of the door
Montero has had a tough season in South Wales so far. The Ecuador international shone at the start, but has since found his opportunities limited at the Liberty Stadium - with him not even in the squad that lost 1-0 to Southampton at the weekend.
With Wayne Routledge ahead of him in the pecking order and Francesco Guidolin seemingly as keen on the player as his predecessor, Garry Monk, was, the winger has struggled to even get chances off the bench this year.
As a result, Middlesbrough sensed the opportunity for a move for the player, who showcased his talent for all to see at the 2014 FIFA World Cup. However, Swansea are in a real scrap for survival at the moment and so are unwilling to let anyone leave the club - even if they haven't played a huge role as of yet.
Montero looking for security
The player himself is believed to be keen on a move away from the Swans, albeit only if it comes with the prospect of a permanent move at the end of the loan.
Playing time appears to be all that he desires, but it seems that he'll have to hope that this comes at the Liberty in the remaining few games as the club do not want to further thin their struggling squad.