Rated at £100m, Tonali is being watched by Arsenal, Juventus and Chelsea this season.
Shearer expects Tonali to leave Newcastle if they fail to clinch European football for next season.
He told Betfair: "Sandro Tonali hasn't hit the heights he was at last season, but I guess what'll happen is, if Newcastle aren't going to qualify for Europe or be competitive in the Premier League, you'd expect other clubs will look at Newcastle and try to buy their best players.
"Although it was a surprise in the January window, I think it'll happen more in the summer if Newcastle don't achieve what they have in the past few years.
"Top players want to play Champions League football, and we know there's no real loyalty in football - I'm not saying Tonali will do anything like that, but we know if clubs don't get into European places, other clubs will try and pick players up.
"Newcastle have to start winning games and go far in the FA Cup and hopefully the Champions League to try and rescue what, at the minute, certainly Premier League wise, has been a disappointing return.
"I know we got to a semi-final and all those years ago we'd craved for that but then the money that's been spent and put into the club and where the club wants to go to, at the minute it's been disappointing."