The Uruguay international is believed to be close to securing an £11.8 million switch to St Mary's Stadium from Bologna.
Inter Milan, Liverpool and Tottenham Hotspur were all linked with a move for Ramirez, but it appears Saints have pulled off a major coup in landing the 21-year-old.
However, the young playmaker is yet to complete his move to the club.
"It looks exciting, doesn't it?" Adkins said ahead of Southampton's first game back in the Premier League against Manchester City.
"I think he has come out in Italy and said it is already sorted, but I think you'll find the policy of the football club is until the player has signed on the dotted line and we announce it then really we try to do everything privately.
"We have been consistent with that over the years and we'll probably stay that way.
"If it is true, then it obviously shows the ambition of the football club. I know the chairman, Nicola Cortese, is very ambitious here and it is great.
"We were in administration a few years ago and we've come a hell of a long way in a short space of time.
"To be linked with players as such - and don't forget we broke the transfer record in the summer when we signed Jay Rodriguez - shows we're very ambitious, but likewise we'll cut our cloth accordingly.
"Having been in administration once, the last thing we'll do is end up in that situation again. The club is run very well, very prudently.
"But we're very, very ambitious and having reached the Premier League now, very quickly, we've got to give ourselves an opportunity to do well there."
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