Leaders Chelsea are seven points ahead of third-placed Arsenal and have the added bonus of a game in hand.
But Arsene Wenger's men are a team in form, having won nine of their past 10 Premier League matches.
Wales international Ramsey is well aware that Arsenal need favours from their rivals, but is remaining cautiously optimistic.
"We just have to focus on ourselves and believe other teams around us will be on the end of upsets," he said.
"We just have to try and win every game until the end of the season.
"In this division teams can lose against anyone. We have just got to be switched on and make sure it doesn't happen to us and maintain this run.
"Stranger things have happened."
Arsenal return from the international break with a match against Liverpool, while the fixture at home to Chelsea at the end of the month is surely must-win for the FA Cup holders.
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