Injury to Matthew Bates after 23 minutes at Crystal Palace on Saturday resulted in 24-year-old McMahon being handed the captain's armband by manager Tony Mowbray.
And with Bates still awaiting the results of a scan on his leg, the right-back looks set to skipper the side again against the Swans a role which McMahon, who lifted the FA Youth Cup in 2004 for Boro, will hold in high regard.
McMahon said: On Saturday, it all happened quickly. Matty went off injured and the gaffer told me to take the armband, so obviously I did you do what you're told.
If he gives it to me on Saturday it will be a massive honour.
You dream of captaining your side, but to be honest I'm not thinking about that.
I just want to play football and stay in the team, but if it came down to me captaining the side, it would be an honour.
However, McMahon's first experience of captaining the first team was not a memorable one James Vaughan scored the decisive goal for Palace after 36 minutes and Boro could not break the Eagles down.
And the Evenwood-born full-back is expecting a different proposition with the visit of Brendan Rodgers' outfit on Saturday.
McMahon said: It was horrible. From start to finish it felt like one of those horrible games. They got the goal from a mistake and they just camped in and got everyone behind the ball. It was hard for us to break them down obviously we didn't do that.
It was frustrating that we'd been on a good run to lose like that, but that's football and we've got to go about it in the right way against Swansea.
It's going to be the opposite to Crystal Palace, they're going to come here and play.
They play good football like we do, so it's going to be a good game.
Boro visited the Liberty Stadium in November and succumbed to a late Scott Sinclair goal to lose 1-0. Boro were not at their best that day, and McMahon has warned the Swans that Boro are now a different outfit almost three months into Mowbray's reign.
He said: It will show how far we've come. Everyone who has come and seen us in the last two months has seen that we have improved since the manager came in. We need to get to that again and it starts on Saturday.
Tickets are on general sale for Boro's next three home games against promotion chasers Swansea, QPR and Nottingham Forest.
Boro host Swansea City on Saturday, QPR on Saturday, February 26 (both 3pm) and Nottingham Forest on Tuesday, March 1 (7.45pm).
Prices for Boro Pride members start at £21 adults, £14 Over-65s and those aged 18 to 21, while all members aged under-18 pay £8.
General sale prices start at £23 adults and £16 over-65, with all under-18s paying £13.
Seats are also on sale for Boro's away game at Millwall on Saturday, February 19 (3pm).
Tickets can be booked online at mfc.co.uk, in person at the Riverside ticket office or MFC Official in Captain Cook Square, or 24 hours a day by phone on 0844-499-1234.