The 21-year-old Uruguayan has been the subject of speculation this summer after impressing in Serie A with Bologna. Inter Milan, Liverpool and Tottenham were mooted as potential destinations for Ramirez, although Press Association Sport understands a move to the Premier League new boys could be completed this weekend.
"It looks exciting, doesn't it?" Adkins said, speaking ahead of Sunday's season opener at 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 very short space of time. To be linked with players as such - and don't forget we broke the (club) 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."
Another wideman Adkins is interested in is Blackpool's Matt Phillips, and it is understood Southampton have made a £6million bid. The 21-year-old has impressed for the Tangerines, whose manager Ian Holloway last weekend pledged to report an unidentified club he claimed made an illegal approach for the winger.
Some reports named Southampton as the team in question, forcing Adkins to deny such a move - a stance he kept on Friday. He said: "We've been linked before with players and it came out last week because Blackpool were obviously weren't happy with something.
"I probably think it's best that I don't make any further comments on that, while people are doing it. I'd like to think we do things properly here at Southampton and I made a comment last week about it and I think if you need to take anything you can take it from that."
Source: PA
Source: PA