The banners were recently displayed in the win over Hull City in the FA Cup.
The Gunners chief has come in for increased criticism in recent weeks, as a poor run of form has seen them fall away in the title race.
They now find themselves eight points behind Leicester City with just eight games of the season remaining.
That is extremely disappointing for Arsenal’s fans, who believe they should be doing much better in a season where their rivals have fallen away.
Indeed, some have shown their displeasure with a Wenger Out banner in the recent win over Hull, but Ramsey says he was shocked to see that.
"It shocked me. I didn't see the banner at the time because I was injured and went straight down the tunnel,” Sky Sports report him saying.
"The lads weren't talking about it because the same sentiments have been expressed before. To think that an Arsenal fan has taken the trouble to bring that to a game does shock me.”
"You see the amount of managers who get sacked these days - a few bad results and they're under pressure. But Arsene Wenger has handled it before and come out of it and I'm sure he'll do so again.”
Should the Gunners fail to win the title this season, in what is arguably a season they should be much closer in, then the pressure will surely be on Wenger.
They do not have the FA Cup to fall back on, having been knocked out by Watford on Sunday, something that has saved them in recent years.
The Champions League is extremely unlikely also given they head to Barcelona with the Catalans leading 2-0 in that tie.
Who though, they could replace him with is the prevalent question, with many wondering if there are any suitable candidates at this moment in time.