Stoneman, 28, has scored 14 centuries in 118 first-class matches, but is yet to receive a call-up for England.
"He's scored a 1,000 runs two years in a row now and people are just starting to mention him." Onions told BBC Sport.
"His volume of runs have made him basically selectable. You have to pick him - pure volume of runs."
Newcastle-born opener Stoneman was named the club's batsman of the year last season, having been one of only five Durham players to feature in every championship game.
"People don't even talk abut him really. He's been on no Lions tours, he hasn't even been involved in any kind of squads," 33-year old Onions added.
"It might be quite hard for him to take that."
But Onions, who has nine Test caps for England, is confident Stoneman will be considered for selection this year, and could put fellow batsmen under pressure.
"I think Mark Stoneman is certainly one of the guys that England will be looking at," he added.
"Whether or not [Alex] Hales is under a little bit of pressure - I think he'll go into the start of the season in a couple of months really having to score as many runs as he possibly can."
Durham bowler Graham Onions says teammate Mark Stoneman has to be picked for international honours based on his "pure volume of runs".