The Italians showed serious interest in the right-back in January, but were unable to push through a deal reportedly worth around £4.8million to the Dons.
With the English Premier League duo interested in Ramsay, The Scotsman understands Bologna are set to return to the negotiation table.
After failing to land the 18-year-old in the winter window, they signed Dutch teenager Denso Kasius for around £3m from Utrecht. However, he has not made the impact they had hoped.
Bologna are no strangers to the Scottish market, having signed Aaron Hickey from Hearts in 2020. The Scotland international is expected to leave in a big-money move this summer with the likes of Arsenal and AC Milan linked with versatile wing-back.
Ramsay is viewed as a possible back-up to Trent Alexander-Arnold at Anfield, while first-team action would be more likely at Leeds.
The teenager had a breakthrough campaign this past season, making 33 appearances and winning the SFWA Young Player of the Year.
Ramsay addressed the transfer speculation in April, taking his name being linked with big clubs in his stride.
“It’s good being linked with big clubs but I’ve just tried to block it out really," he said. “You can’t get caught up in all of that. That’s the worst thing, especially as a young player.
“I’ve just broken into the first team this season, so I’m trying to block it out and keep playing my game. If you come into the first team and play well, like I have, anything can happen.
“The likes of Aaron Hickey came in at Hearts. He did well and got a big move to Serie A and he’s been brilliant, scoring goals and everything.
“Andy Robertson at Liverpool and Tierney at Arsenal, they’ve all been brilliant and they’re players I look up to, especially as they are full-backs like me.
“I’ve seen what they’ve done. I feel I could go on to do that as well."