Rafa Benitez has confirmed his interest in the Chelsea job after he emerged as the favourite to succeed Roberto Di Matteo.
Di Matteo was relieved of his duties on Wednesday morning and Sky Sports understands Benitez is the man being targeted.
Benitez spoke from Abu Dhabi, where he was attending a coaching seminar, before flying to London and admitted he was waiting for a club who can win trophies.
"I have just found out [about Di Matteo]. Obviously Chelsea is a top side and they can compete for trophies so it goes in this category," he told Sport360.
Asked if he had already spoken to Chelsea, he added: "You ask directly, I cannot answer directly.
"In football a lot of people are talking so we will see what happens in the next few days. I am looking for a club that can challenge for trophies and Chelsea is one of these clubs."
Benitez is known to have spoken to Chelsea in the summer but backed away as they were only willing to offer a one-year term, with Pep Guardiola - currently on a sabbatical - tipped to take charge.
But the former Liverpool boss seems more open to the prospect, saying: "I have to talk with my agent and see what he has been doing the last couple of days.
"But I am just trying to go to a team that can win. So we will find ways to have a challenge like this."
The hosts had dominated for lengthy spells, twice being denied by the woodwork as well as having two efforts cleared off the goal-line in the League One clash at the Broadfield Stadium.
However, a last-minute own-goal from substitute David Hunt, who headed past helpless goalkeeper Paul Jones from eight yards following a corner from Jamie McAllister, handed the points to the Glovers.
Barker said: "There are 20 games to go and you get highs and lows like this all season. The important thing is how you react to them. We have only taken one point from our last two home games but we have not lost back-to-back games and must maintain that.
"We've only lost three of our last 11 matches so you can't really say that is a sticky patch. It was an excellent reaction. We played a great tempo on a difficult pitch and tried to play in the right areas.
"Unfortunately, it wasn't our day. The players are down. The character was great on Saturday whereas here the performance was fantastic."
The home side cruised to back-to-back wins at the Proact Stadium through goals from Chris Atkinson, Sam Togwell, Marc Richards and Jack Lester with Kaid Mohamed replying for the visitors.
It was another bleak away day for Cheltenham, who were also beaten at Rotherham on Saturday, and Yates said: "We have gifted them goals at the wrong time and didn't execute what we were trying to do particularly well.
"We got back to 2-1 and should have built on that but within minutes we were back to a two-goal deficit and chasing the game again.
"The players are hurting because no one likes to lose two games on the spin. We are third in the league and we're not going to hit the panic button but we have to go back to basics and be strong, competitive and organised.
"We have to get back to doing what we are good at. For the last couple of games, we've not done that and we've been found wanting."
