After signing four new players; Mark Sykes, Kal Naismith, Kane Wilson and Stefan Bajic, their next steps are to recruit a new centre-back and defensive midfielder.
Allen this summer helped Wales qualify for their first World Cup in 64 years and is likely to start for the Red Dragons in Qatar.
But whilst he was turning out for his country, his club future was uncertain and City were one of the clubs interested in taking him.
It has now emerged that they made a move for the vastly experienced player, who has played in both the Premier League and the Championship.
Ahead of a return to Swansea, the club he started his career at before a then record sale to Liverpool, City made an attempt to sign him.
WalesOnline report that Bristol City wanted to bring him to Ashton Gate but could not put together a suitable wage package for the player that would work for both parties.
There was also an offer from Spanish outfit RCD Mallorca, who finished 16th in La Liga last year, but again that was an option that was not explored.
The 32-year-old is a former teammate of City player-coach Andy King and the pair would have played with one another a number of times, including at EURO 2016, but a reunion will not be happening.
Allen rejected an offer to stay at Stoke City, having been there from 2016, after penning a five-year contract when the Potters were in the Premier League.
He now looks all but set for a return to South Wales with a medical planned for Friday afternoon after terms were agreed and he could play in their friendly against Plymouth Argyle on the weekend.
The sale of Flynn Downes to West Ham United, which could see them coup up to £12m has meant that they have resources to sign the player.
They had also needed to add more midfield bodies after former Bristol City midfielder Liam Walsh ruptured his Achilles in a pre-season friendly against Haverfordwest County last week.
Walsh, who was at City for three years, but failed to make a mark, is set for an extended spell on the sidelines and has endured a difficult time since departing the West Country a year ago.
The 24-year-old is to undergo surgery and it is the second major injury issue he has had with the Swans after injuring his hamstring at the start of the 2021/21 campaign.
Walsh, signed by Steve Cooper before his departure on the eve of the new season was unable to force his way into new bosses Russell Martin’s plans and he was later shipped out on loan to Hull City, but made just three appearances.
WalesOnline say that Swansea were willing to offload the midfielder just a year into his contract but with a spell out, he will stay with them until he recovers.
Korey Smith, who like Walsh has also made that route across the Severn Bridge, remains without a club after his contract expired with them this summer.