Liverpool believe they are in pole position to sign Ashley Williams from Swansea City this summer despite the prospect of a bidding war with Arsenal.

Arsenal, it can be revealed, had a £9m offer for the Wales captain rejected by the League Cup winners in January. They are expected to return with a higher bid at the end of the season as Arsène Wenger seeks an established leader for his central defence but Liverpool, despite the threat of failing to qualify for Europe next season, are confident of luring Williams to Anfield.

One factor is Brendan Rodgers, under whom Williams worked happily for two years at Swansea. The defender was also a boyhood Liverpool fan – John Barnes was his favourite player – and the Anfield club believe he would favour a move to Merseyside over Arsenal. Potential problems for Liverpool, however, are the defender's age and price-tag.

Williams turns 29 in August and Fenway Sports Group, Liverpool's owner, has pursued a youthful transfer policy since Rodgers became manager. Oussama Assaidi is the oldest player that Rodgers has signed as Liverpool manager, the Moroccan winger arriving days after his 24th birthday.

Swansea, as their stance with Arsenal in January demonstrated, will also hold out for more than £9m for their key defender. Rodgers may have to persuade FSG to part with closer to £12m for a player who does not fit their age profile but meets Liverpool's obvious need for an established defensive leader.

Liverpool could require three central defenders this summer with Jamie Carragher retiring, Sebastián Coates available for transfer and Martin Skrtel falling out of favour with Rodgers. A priority for the Liverpool manager is to land his key targets early.

"I think it's very important to get players in as quick as we possibly can," he said. "I think we will be in a much stronger place [than last summer] because we have much of the structure of the team already done so it's about sprinkling more quality into it and a bit more depth and I'm confident we can do that. Everyone is working very hard and everyone is in unison with what we are trying to do. I believe if we get some good work done early it helps start well at the start of next season."

Rodgers oversaw an underwhelming summer in the transfer market last year when his recruitment team of Dave Fallows and Barry Hunter – the head of recruitment and chief scout respectively – were placed on gardening leave by Manchester City, their former employers.

But he insists: "The recruitment team has regular meetings now to establish where we are in terms of the targets. There is a process we go through and there is still some work to do and I am confident we have a pattern of work, the players are there and it's about the availability and the players we can afford."