The two sides face each other this Saturday at the John Smith’s Stadium (kick-off 3pm) with both on the same number of points (30) but with the Swans lying 13th in the table and Town 15th, courtesy of goal difference.
And while David Wagner has claimed two wins in the last three Premier League games, Carlos Carvalhal has orchestrated a remarkable turnaround in the South Wales’ fortunes.
The Portuguese boss has breathed new life into the side, picking up 17 points from his nine games in charge – in stark contrast to claiming only 12 from the season’s first 18 game under Paul Clement.
Jenkins, who had a five-year spell in South Wales before going on to make 258 appearances for Town between 1995 and 2003, believes momentum is key for both sides in their top-flight relegation battle.
“When you are on a winning run football becomes easy, but when you haven’t got it then it becomes one of the most difficult games to play,” said the former full-back who is now assistant manager at Hereford FC.
“It’s especially important when you’re fighting for survival – that little bit of momentum over three, four, five games to get the points needed.
“I think it will go down to the wire, but if you can get a few back-to-back wins it will shoot you up the table – you just have to look at what Swansea have done in that respect.
“Before Carlos Carvalhal, everybody said they were doomed and down – but he’s gone in and got some momentum going and they are on an incredible run.
“Looking at Swansea, I think they will be safe and I have no doubt Huddersfield will stay up as well.”
Jenkins, more than most, knows how crucial momentum is for a side, being part of Steve Bruce’s Town side who were top of the Old Division One in December of the 1999-2000 season before spectacularly dropping off in the run-in after the sale of star striker Marcus Stewart.
Reflecting on that experience, Jenkins said: “It was a strange situation really, we were in a great position at Christmas and perhaps the sale of Marcus Stewart to Ipswich Town saw us lose a lot of momentum.
“We obviously lost his goals and him and Clyde Wijnhard had a fantastic partnership which was broken up – and we didn’t quite get the goals after that.
“It had a big impact and, in the end, we probably weren’t good enough over the course of the season, but I think if Marcus had stayed we definitely would have made the play-offs.”
Now 45, Jenkins added of the upcoming match: “Obviously it’s a huge game for both teams, when you are playing teams in and around you it’s the proverbial six-pointer.
“But I have no doubt, regardless of the result on Saturday, that both teams will stay up.
“That would be the perfect scenario for me as well as I spent a lot of time at both clubs and nothing would please me more than to see the two sides stay in the Premier League.”