The 22-year-old Nigerian, who has been with the club since the summer of 2020, has been very impressive this season.
Bassey is a key reason for the team's success in Europe, where they reached the Europa League final and lost on penalties to Eintracht Frankfurt.
"There do seem to be a lot of rumours. If there's another incredible bid from down south, it's difficult to stop that," McLeish said as quoted by Football Insider.
"He's becoming a sought-after component and rightly so with his performance levels. So much so there's interest outside of Rangers who would obviously like to have him in their team. That country just happens to be over the border in England.
"They will also be aware that if someone comes in with a monstrous bid for him, it can help them recruit more players. Obviously, they would need to fill the void that he leaves and he's proven to be a very versatile player."