The Swans beat Hull City 3-1 on Saturday and currently sit eighth in the Premier League table.
The current team is on course to beat the record set by the Class of 2012-13, who finished ninth in the division with Michu leading the way with 22 league goals.
Williams, however, is looking further back than that and wants this year’s vintage to pass the mark set by the 1981-82 team, who finished sixth and topped the table at several points of the campaign.
“We just want to continue to get as many wins as we can and see how high we can finish,” he said. “We want to try and get the best Premier League finish in the club’s history.”
If they are to achieve such a feat, Swansea will need Bafetimbi Gomis to maintain his recent goalscoring form. The brace he scored against Hull took the Frenchman’s tally for the season to just eight but he has scored three in his past two outings.
Gomis is also on the road to physical recovery after collapsing in the game against Tottenham.
“I’m pleased for him,” said Williams. “He’s obviously playing with a lot more confidence than he was. He’s worked so hard to get through that and start scoring.
“He had a tough weekend a fortnight ago but he got the goal in the end and he’s built on that today. All the lads are pleased for him because we know how hard he works day-in and day-out.”
Swansea gave a debut to 19-year-old Matt Grimes, a £1.75m January transfer window signing from Exeter City, in the win over Hull and the teenager said it felt like a dream come true to make his Premier League bow.
“It’s unbelievable,” he said. “It’s every kid’s dream to play in the Premier League. Thankfully I have done that today and I just want to thank everyone at the club for welcoming me.
“Obviously it’s a great feeling for me and my family and I’m just hoping to push on. I’m not really thinking too far ahead.
“I have made my debut now so the next step will be to start a game and make my full debut. I’m looking forward to doing that and I’ve just got to keep my head down and keep pushing.”