The Canada national team captain has been linked with a return to the English Premiership, with Crystal Palace and Southampton both keen on acquiring the former Burnley man’s services.
But speaking ahead of his side’s clash with Hibs at Ibrox on Sunday, Gerrard said: “I don’t want to lose Scott, it doesn’t surprise me that clubs are interested.
“Every single player has a price but he knows very well I want him to stay here at Rangers.”
Arfield added: “Over the last two years I haven’t played enough football.
“Playing [at Rangers] is the happiest I have been in years, wearing this badge, and my family is settled here.”
Addressing the debate over Ryan Kent’s future, and a potential return to Ibrox, after the on-loan Liverpool winger admitted he was “tired” of changing clubs every season, Gerrard added: “Ryan is a possibility but it is probably too early for him to make a decision.
“Ryan knows we want him as do Liverpool but he will have a big decision to make as teams will be queuing up for his services.
“My advice to Ryan is to go where you will be happy.”
After the transfers of Steven Davis on a permanent deal from Southampton and Jake Hastie on a pre-contract from Motherwell were confirmed, Gerrard said it was “important to have a good mix of age and experience in the squad”.
He continued: “Steven Davis is playing regularly - you can see him hitting top form and we are pleased for him. With a full pre-season under his belt he will be ready to help us challenge next season.
“We want competition for places, Jake [Hastie] is coming in to help us add answers in the final third.
“He is a young lad and we will need to treat him with patience.”