Libby went missing in the early hours of February 1 after a night out with friends.
Her body was discovered in the Humber Estuary on March 20.
In a message released through Hull Community Church, her mother Lisa expressed her gratitude for the “love and kindness” shown by people in the Yorkshire city.
She said it had brought “comfort” to her and Libby's father Russ during what has been a “horrendous” time for the Squire family.
The church said Libby's family were hoping the bench she was last seen at would become a commemorative location.
It has been adorned with flowers and colour - although Libby's family have requested no photographs of her are used.
The statement said: "Lisa and Russ’s vision for the bench is that it will become a safe space for everyone.
"As the years go by, they hope it won’t be remembered as Libby’s bench, but just known to be a safe, well-kept space in the neighbourhood.
"Libby’s sister talked about a friendship bench at her school, where children who were sad or lonely or having a bad time, can go to the bench, and someone will see them and offer help.
"She said that often somebody would just sit with them, sometimes not even talking.
"What a beautiful picture of how this bench could become.
"A place of friendship, kindness and safety."
Earlier this week, it was revealed that Libby’s parents cannot lay their daughter to rest yet as the police are yet to release her body.
Her death remains a homicide inquiry and an investigation into how she died is ongoing.
In a statement, a spokeswoman for Humberside Police said: “Inquiries are ongoing into the death of 21-year-old University of Hull student Libby Squire.
“We continue to investigate Libby’s death as a homicide, with further work and analysis being conducted.”