Ellen had been reported missing by her family at 7.20pm on Friday evening when she failed to return home from college.
Police said a 47-year-old man from the Billinge area was taken into custody on Sunday for questioning.
According to Manchester Police, the body of an unnamed 18-year-old girl was found in Wigan's Orrell Water Park at 2:30am local time "on the edge of a field".
Detective Superintendent Howard Millington, form GMP's Major Incident Team, said: "First of all my thoughts are with the woman's family at this devastating time".
Police say a 51 year old was arrested in Preston. They said her disappearance was very out of character.
Police said a post-mortem test concluded her death was caused by "multiple wounds to the neck".
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The shooter was an IL man, James Hodgkinson, who had lashed out against President Donald Trump and Republicans over social media. FILE - In this March 8, 2017 file photo, House Majority Whip Steve Scalise of La. speaks on Capitol Hill in Washington .
A teenager who was found dead in Orrell Water Park following a brutal attack died from wounds to the neck.
"We are also working with Wigan Council and Winstanley College, where Ellen was a pupil, to ensure support is in place for anyone affected by this shocking incident".
"We will be supporting our students, many of whom are Ellen's friends and her Winstanley family, in every way we can as we come to terms with something no one should ever have to come to terms with".
"We would encourage the public to continue getting in touch, as said before, this investigation is still in it's early stages". Our specially trained officers are with her family and will continue to support them through this hard time.
He added: "Myself and my team will not stop until we have found out exactly what happened and have brought whoever did this to justice". If you have any concerns, please speak to our officers.
Anyone with any information is asked to contact police on 0161 856 7103, alternatively call 101 or the independent charity Crimestoppers on 0800 555 111.