Gibbs' £15m (€16.3m, $19.2m) price-tag and his wage demands forced Watford to direct their attention onto other targets and has also put off a number of potential suitors, including Bournemouth, Newcastle and Brighton.
West Bromwich Albion, meanwhile, swiftly ended their interest earlier this summer after having a bid for the 27-year-old rebuffed.
However, according to the London Evening Standard, Arsenal are now considering accepting £7m for Gibbs and have told the left-back, who has only 12 months left on his deal, that he is free to leave this summer.
The London-born defender graduated to Arsenal's senior squad in 2007 but has only started 11 Premier League matches over the last two seasons after falling behind Nacho Monreal in Arsene Wenger's plans.
Gibbs' camp has held talks with a number of Bundesliga clubs and Galatasaray but it is understood that the player would prefer to remain in the Premier League.
Alongside Gibbs, a number of first-team players are not in Wenger's plans for the upcoming campaign, but are yet to secure a move away.
The Arsenal manager admitted last week that he needs to offload a few players before the end of the month, as only Wojciech Szczesny, Gabriel Paulista, Yaya Sanogo and Emiliano Martinez have left the Emirates so far this summer.
However, Wenger did not rule out the possibility of Jack Wilshere earning a new contract at the club, although it admitted he might have to prove himself on loan at a different club first.
"You know how much I love Jack and his talent, I started him at the age of 17 but today in the football world you need to be a consistent presence," Wenger told reporters during a press conference held prior to Arsenal's heavyweight Premier League clash with Liverpool on Sunday (27 August).
"What is at stake for Jack is not his quality, his talent or his determination, it is whether he is a consistent presence at the top. I hope he can manage to do that and after nobody questions his quality."
"I'm open, you know, with Jack. We have honest conversations and I'm open to what is the best for him. He is at the stage of his career where he needs to play and I can guarantee him today that, and I think I'm quite open on that."