Murphy is currently a free agent, having left Cardiff City earlier this summer following the expiry of his contract with the Championship club.
Having joined Cardiff from Norwich back in the summer of 2018, Murphy made 99 appearances and scored 14 goals in all competitions for the Bluebirds, before spending the second half of last season on loan at Preston.
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But after completing a permanent exit from the Welsh capital this summer, Murphy has been on trial with Oxford as he looks to find himself a new club.
Now it seems as though the 27-year-old has indeed done enough to earn a deal at The Kassam Stadium.
According to this latest update, Murphy is now undergoing a medical with Oxford on Tuesday, having agreed terms on a deal with the League One club.
If confirmed, Murphy could become Oxford’s fifth signing of the window, and would follow Ciaron Brown in joining Oxford after leaving Cardiff this summer, the left-back having had a spell on loan with the U’s last season.
This could be a rather good signing for Oxford United if they do indeed complete a deal for Murphy.
The winger has plenty of Championship experience and pedigree, that has even given him the chance to impress in the Premier League at times.
As a result, you do get the feeling that he should be capable of making an impact in League One, especially considering how he previously impressed under now Oxford manager Karl Robinson during a loan spell at MK Dons.
On a free transfer, this should work well financially for Oxford as well, meaning the League One club could be about to complete a smart piece of business here.