Arfield’s current deal expires at the end of the season and the 33-year-old is free to speak to other clubs.
But van Bronckhorst is hopeful of retaining the services of a player who continues to make valuable contributions such as the winning goal he scored after coming off the bench against Livingston at Ibrox on Wednesday night.
“Scott has been really important for the team, not only this season but all the seasons before as well,” said van Bronckhorst.
“He is an experienced player and he is definitely a player I want to have longer to be at Rangers. Hopefully we can welcome him next season as well.”
Arfield was one of Rangers’ first signings under van Bronckhorst’s predecessor Steven Gerrard in the summer of 2018 and the former Falkirk, Huddersfield and Burnley player has scored 32 goals in 165 appearances for the Ibrox side. He retired from international duty with Canada earlier this season in order to concentrate on prolonging his club career at the highest level possible and has previously expressed his own willingness to extend his stay at Rangers.
He is one of eight members of van Bronckhorst’s first team squad who are out of contract at the end of the season. The others are goalkeepers Allan McGregor, Jon McLaughlin and Andy Firth, defenders Connor Goldson and Leon Balogun, midfielder Steven Davis and winger Brandon Barker.