The 22-year-old has joined the Premier League club on loan until the end of the season from Hoffenheim, where he played alongside current Newcastle forward Ba.
The Senegal forward has made a huge impact since leaving the Bundesliga club for the Premier League in January of last year, scoring seven goals in 12 games for West Ham before finding the net 15 times in his 19 games for the Magpies, including his stunning effort in their midweek win over Manchester United.
Swansea manager Brendan Rodgers has spoken of Sigurdsson's impressive goalscoring ability - the midfielder grabbed 21 goals for Reading two seasons ago - as a factor in his decision to bring the player to the Liberty Stadium, and the Iceland international is eager to mirror the impression made by his friend Ba.
He said: "Demba has been doing alright and has scored quite a few goals.
"He is a good friend of mine who I speak to a lot. He is very happy with life at Newcastle and in the Premier League. He has made a big impact and I hope I can do the same here at Swansea.
"We are playing Newcastle when he is back from the African Nations Cup and he is already looking forward to the game. He told me the league is fantastic and he is loving it here.
"He told me he loved the way that Swansea play football, especially the way they keep the ball for long periods.
"He has scored 15 goals so I don't know if I can score that many, but hopefully I can chip in with a few and help the team get some points.
"I have set myself a target for the rest of the season but I will keep it to myself."
Sigurdsson was handed his first chance at Reading during Rodgers' short stint with the club in 2009, and the Northern Irishman left such an impression on him that it was an easy decision to overlook interest from Aston Villa and the Royals to move to the Liberty Stadium.
"There were a couple of other clubs interested," he said. "But as soon as Swansea showed interest I made my mind up straight away. Brendan called me and tried to persuade me - but I told him I had already made my mind up so I didn't need any persuasion.
"I haven't played much because I missed two months of pre-season after being injured with the Under-21s and haven't had many chances so it only took a couple of days for the clubs to agree the deal and hopefully I can gel in quickly and get going."
And with his injury and a change of manager at Hoffenheim having limited his time on the pitch this season, Sigurdsson is desperate to be involved at Oakwell, particularly in a competition he has fond memories of watching while growing up in Iceland.
"It would be fantastic to play," he said. "It has been hard not to play and just train. I had my knee injury but I saw a specialist in Germany and he managed to sort the problem and the pain has gone away.
"When I was growing up everyone watched the FA Cup in Iceland, it's a great competition."
Although Premier League survival is Swansea's goal this season, manager Rodgers had made it clear he will not be taking the FA Cup lightly, and wants his side to show they have learned from the disappointment of their 3-1 Carling Cup second-round defeat at Shrewsbury in August.
"Barnsley will be a tough game, Keith Hill has done a great job there, and we will respect the nature of the game and select a strong side," he said.
"Against Shrewsbury it was disappointing because we were a newly-promoted side and a lot of our players had come up from the level Shrewsbury are at, but that night allowed the players to see we were not going to take our foot off the pedal in any game because we are not good enough to do that
"We have to be at our maximum and I think you will see a different mentality this weekend."
