Wales international Ramsey is set to complete a free transfer to the Serie A champions at the end of the season, having agreed to a contract that, according to some reports, will see him earn £400,000 per week.
The 28-year-old, who could miss the rest of 2018-19 due to a hamstring injury, has won three FA Cups since joining the Gunners in 2008, but a shot at the Premier League title has rarely looked likely.
However, Seaman still believes the Londoners are a bigger club than Juve, who have won eight consecutive league titles in Italy and have reached the Champions League final twice in the past four years.
"Arsenal will remember Aaron Ramsey with great fondness," Seaman told talkSPORT. "He's a great player and the most frustrating part about all this is he's playing even better now, and he's going to leave!
"It's the same thing again, another great player is leaving our club to go to another club which is not really as big as Arsenal.
"For me, it's so frustrating that they couldn't do that deal [for a contract extension]. He'll probably get voted player of the year."
🗞 Our medical team have provided updates on...— Arsenal FC (@Arsenal) May 1, 2019
■ Denis Suarez
■ Aaron Ramsey
■ Nacho Monreal
Arsenal have endured a mixed 2018-19 campaign which could yet end with them failing to qualify for the Champions League.
Unai Emery's men are currently fifth in the Premier League table, two points behind fourth-placed Chelsea with two fixtures remaining.
Next up for the Gunners is a Europa League semi-final tie against Valencia on Thursday night and winning the trophy may now be their best chance of earning a place in the top tier continental competition next season.
Ramsey has been ruled out of the first-leg clash, having been forced to miss Arsenal's last three games with the injury he suffered against Napoli in the quarterfinals.