The offer came due to Wolves only having around £20m to spend this window.
Ramsdale, 26, has made 89 appearances for Arsenal since joining from Sheffield United in 2021 for an initial £24million fee.
The England international had enjoyed a strong debut season at the club and was named in the PFA Premier League Team of the Year for the 2022-23 campaign.
Wolves are keen on a deal to sign Arsenal goalkeeper Aaron Ramsdale ahead of the deadline
Ramsdale lost his place in the Arsenal starting eleven last season to David Raya and has remained Mikel Arteta's No 2.
The 26-year-old is eager to play regularly again and has attracted interest during the summer.
Newcastle had enquired about Ramsdale earlier this year but Arsenal's asking price was then deemed prohibitive yet they are now considering lower offers to allow goalkeeper to kickstart his career.
The Gunners have lined up Espanyol's Joan Garcia as his possible replacement.
Johnstone is another option for Wolves having been stripped of his No 1 shirt at Crystal Palace this summer.
Dean Henderson, who wore the No 30 last season, was given Johnstone's shirt number in an indication he will be first choice under Oliver Glasner.
Johnstone, who spent the majority of last season as the Eagles’ preferred goalkeeper, has been on the bench for Crystal Palace's opening two Premier League matches.