Coleman is expecting to accept the offer of becoming the next manager of Real Sociedad, according to his representative.
The 37-year-old, sacked by Fulham in April, is "enthusiastic" about the prospect of taking over the Basque club, who were relegated from La Liga earlier this month.
Alan Smith told Sky Sports News: "They are very keen to sign him."
Smith, manager of Coleman's former club Crystal Palace from 1993-95 and 2000-01, continued: "I think they've made as good an offer as they're going to.
"Now it's just a case of Chris sleeping on it - he's got to decide if this is the type of place he wants to be for the next couple of years.
"He's seen the current president and the one who's going to be here next year - it's really a case of Chris saying 'I want to come here'.
Smith revealed that Wales coach John Toshack, himself a former Sociedad boss, has been instrumental in the job offer.
He continued: "They've really pushed the boat out. John Toshack has recommended Chris - he's been very positive.
"John Toshack is still a major hero out there and it's a magnificent club. When you see the training facilities, it doesn't get much better.
"Chris has spent the last couple of days here and seen everything they have to offer.
"There don't appear to be any drawbacks - it's just a case of if Chris moves here - and I'd say the odds are pretty favourable."
Smith continued on Sky Sports News: "They'd like to know by July 1 at the latest.
"The players start back from training on July 16 - he's got to make his mind up fairly quickly.
"There's a little bit of pressure on him to sign - but he's got to be settled.
"He's never made any secret of the fact he'd like to coach abroad and I suspect this is not going to be an offer that's about too many times.
"I think our feeling in general terms is it (the Sociedad offer) is difficult to refuse.
"It's just a question of him sleeping on it and making sure he's taking the right decision.
"But he looks very enthusiastic about it. He was taken aback when he saw the training ground and enthusiasm of the people here."