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The Swans boss wants to hand the centre-half a short-term deal in January.

Birnbaum plays for DC United - the MLS club owned by co-Swans owner Steve Levein - and is free to sign for two months.

Struggling Swansea have conceded 26 goals this season - the second worst in the Premier League.

But Birnbaum, 25, would add experience and organisation to a shaky back-four.

Bradley is chasing other new blood during the MLS off-season with Sporting Kansas City defender Matt Besler another potential recruit, if he fails to bring Birnbaum to Wales.

Meanwhile, defender Neil Taylor admits the next month will make or break Swansea’s season.

The second-from-bottom Swans face relegation rivals Sunderland, Middlesbrough, West Ham and Crystal Palace between now and January 3.

And Taylor said: “We have an important spell coming up.

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“We played nearly all the top sides and haven’t got anything.

“It was a tough time and we didn’t build up any confidence.

“After Christmas that is where you tend to see where sides are going to be towards the end of the season, so this will be very important.”

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Swansea are still on a high after two injury-time goals from Fernando Llorente sealed a sensational 5-4 victory over Palace.

It was Bob Bradley’s first win since taking over and lifted Swansea off the foot of the table.

Taylor added: “If Bob had any hair he would have lost it during the closing stages of that game.

“I don’t think he saw his first win coming that way, but we are happy for him and the staff because there has been a lot of hard work going on. We have got the win, it is the monkey off our back and we need to push on.”