The Chester City striker admitted he had agreed to talk to club management in Ireland to discuss personal terms and was travelling to the League of Ireland Premier Division outfit today.
Both clubs have agreed a fee for the forward and Murphy was making the trip across the Irish Sea in a bid to agree personal terms.
He said: "I've had preliminary talks with club officials at St Patrick's Athletic, and I'm going over to Ireland today to discuss more details.
"I first heard about St Patrick's interest in me on Saturday - it was totally out of the blue. I was surprised, but you never know what's round the corner in football.
"I'm open to anything at the moment that may be beneficial, and I've got to think about my family's and my own future.
"I have to look after my family and myself, but if I do leave Chester it will be sad - it's always sad to leave a club after being there for a while.
"Chester have a good squad and if things don't work out in Ireland I still could end up at Chester this season."
St Patrick's finished second in the League of Ireland Premier Division last season and they currently lie second in the table this term.
They currently lead Latvian club, JFK Olimps Riga, 1-0 after the UEFA Cup first qualifying round first leg tie.
Murphy, 31, who started his footballing career at Chester in 1995, joined Blackpool where he scored 103 goals in all competitions before going out on loan to Macclesfield in October 2006.
The loan at the Moss Rose club was made a permanent deal the following year and he went on to score nine goals in 32 appearances for the Silkmen.
Murphy rejoined Chester 12 months ago and has scored nine goals in 39 appearances for the Blues.
If the Whiston-born forward does decide to join St Patrick's Athletic, Chester may be forced to recall trialist Trevor Benjamin to the club.
Benjamin pulled out of the pre-season friendly against Carlisle last week because of an eye problem in the warm-up.
Davies said: "We need to get a couple of bodies going the other way before we can start to think about bringing anybody else in. Trevor Benjamin wants to come to Chester despite receiving offers from other clubs.
"If I receive the green light to see him on trial again I would bring him back, but bringing in another goalkeeper is a bigger issue at the moment."
Meanwhile, Davies is aiming to see his side take another important step tomorrow night towards their preparations for the new League Two campaign.
The Chester City boss sends his new-look squad into action against newly-promoted Championship club, Swansea City, at the Deva Stadium, (7.45pm kick-off).
The South Wales club are managed by former Blues skipper, Roberto Martinez, who is expected to receive a warm reception from the City fans.
Davies said: "I'm keeping a close eye on who is available for tomorrow's match.
"A few of the players have picked up slight knocks including Paul Linwood and Anthony Barry.
"Paul has had a problem with a back muscle and I'm concerned about him not getting minutes on the pitch, but we all know what he can do.
"My main concern is that he's ready for our first league game at Dagenham and Redbridge.
"Anthony may be rested because he's had a tight hamstring in training.
He's not pulled the hamstring, but we're concerned and we may leave him out of the Swansea match and see how he is for Saturday's match at Telford."
Davies admitted he was looking forward to the game against Swansea.
He added: "Swansea is an attractive fixture and it's been good to see Roberto Martinez having a successful time as Swansea's boss.
"We'll be trying to play to the best of our ability, just as we did during the first half in our friendly against Carlisle.
"Our fans could see on that occasion that we can play attractive, passing football. We held our own against a side from a higher division.
"We'll be giving it another go against Swansea, so I hope we can continue to impress.
"Our six new signings have fitted into a decent squad of players and I just hope now that our fans can pack the place and back us, just like Stephen Vaughan has backed me and this club."
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