Ramsdale is still on the books of Sheffield United but has been the subject of at least one bid from Arsenal turned down by the Blades.
The 23-year-old has suffered back-to-back relegations with Bournemouth and Sheffield United in the last two seasons but is still regarded as one of the best young goalkeepers in England.
Ramsdale was one of England manager Gareth Southgate’s back up options at EURO 2020 although he is yet to make an appearance for his country at senior level.
Having trained with Ramsdale at Bournemouth, Begovic has seen enough of the former AFC Wimbledon man to be convinced that he can make it to the very top.
"He can become one of the best, especially in the country,” the Bosnia and Herzegovina international told talkSPORT.
"He’s already proved that he can play at the highest level. He’s got a lot of potential still to fulfil.
"The more he plays, the more he’s going to progress. So I’m not surprised to see him linked with some of the top clubs.
"What he’s done over the last couple of years shows everyone the quality he has.
"With his age, where he’s at, the potential is there to become an even better goalkeeper."
