"We recognise fully where Matt and his people are coming from and I'm sure they understand our position," Scholes told BBC Radio Stoke.
"We've made Matt a very good offer and I'll be meeting his people again soon."
Etherington joined Stoke from West Ham in January 2009 and has scored seven goals in 52 appearances.
He helped the Potters avoid relegation in his first season at the Britannia Stadium, and then was a key member of the squad that finished 11th in the Premier League last season.
Such was his form, Etherington was tipped for a call-up to the England squad by Stoke manager Tony Pulis.
Scholes added that while the club want to keep hold of their best players, the Potters will not be held to ransom over players' contract demands.
"We've got to find a balance with these things," he continued. "We'd always like to give players whatever they want to keep them at the club, but some clubs have gone down that route and it's not led to a good end.
"It's our job to make sure that we reward people appropriately, but also that we don't get carried away."
Source: BBC Sport
Source: BBC Sport