Central Scouting made them the top-ranked skaters in its final ranking of prospects this season.
The NHL draft is June 30 in New Jersey's Prudential Center.
The lottery to decide order of selection for the first 14 picks is scheduled for Monday.
Jones had 14 goals and 42 assists in 61 games for the Winter Hawks this season.
The Texan was the youngest player on the U.S. team that won the gold medal at this year's world junior hockey championship in Ufa, Russia.
Jones is the son of former NBA player Ronald (Popeye) Jones.
The younger Jones could be just the seventh American player taken first overall in the NHL draft following Patrick Kane (2007), Erik Johnson (2006), Rick DiPietro (2000), Bryan Berard (1995), Mike Modano (1988) and Brian Lawton (1983).
No Finnish-born player has ever gone first overall in the draft.
Barkov, a six-foot-three centre from Tampere, had 21 goals and 27 assists in 53 games for Tappara. He also scored three goals and had four assists for Finland at the world junior championship.
Halifax Mooseheads linemates and Canadian junior teammates Nathan MacKinnon and Jonathan Drouin are ranked second and third respectively in North America.
Central Scouting picked Mooseheads goaltender Zachary Fucale as the top North American goaltending prospect. Furcale had 45 wins and ranked second in the Quebec Major Junior Hockey League with a 2.35 goals-against average.
Finland's Juuse Saros was the top-ranked European goaltender. He posted a 1.86 GAA and a save percentage of .933 with HPK's junior team.
Sault Ste. Marie Greyhounds defenceman Darnell Nurse and Ottawa 67's centre Sean Monahan round out the top five North American prospects.
Central Scouting's final rankings include the top 210 skaters and 35 goaltenders in North America as well as the top 130 skaters and 10 goaltenders from Europe.Suggest a correction