Howson was reportedly not looking to sign Curtis Sanford as one of them, as the 32-year-old agreed to a one-year contract with Yaroslavl Lokomotiv of KHL on Monday.
The GM wasn't disappointed to hear that Washington Capitals veteran goalie Tomas Vokoun had signed with the Pittsburgh Penguins either, allegedly having little interest in acquiring the 35-year-old.
Though Howson has not completely shut the door on Mason, it is believed that the 24-year-old will be kept as a backup or be placed on waivers and perhaps eventually sent down to the minors.
Mason, who struggled mightily in the season, posting a .894 save percentage and 3.39 goals-against-average, is not likely to get traded due to his $3.2 million cap hit next season and his poor performance.
As for youngster Allen York, the 22-year-old performed well in the 11 games he started in at the NHL level, posting a .920 save percentage and 2.30 goals-against-average, but isn't likely to be trusted with the heavy workload of a starting netminder just yet.
The Springfield Falcons of the AHL are also targeting York to play for them next season, which is expected to be more beneficial to the young goalie.
"We see him as (an organizational) No. 3 or No. 4 at this point in his career," Howson said.
While Howson keeps looking for a netminder, many could suggest the possibility of chasing after Vancouver Canucks' Roberto Luongo, who is willing to waive his no-trade clause.
However, his 10-year contract at a $5.33 million cap hit is most likely too much of an obstacle for the Jackets, while Luongo is not expected to agree to move to Columbus as the Jackets haven't been much of a contender in the past several seasons.
Howson could have a look at Nashville Predators' backup Anders Lindback, who is slated for restricted free agency this summer, though an inter-division trade could be challenging.
Meanwhile, Los Angeles Kings' backup Jonathan Bernier could also be a good option, though Howson has never expressed a great deal of interest for the 23-year-old.
The GM could also look into Philadelphia Flyers' Sergei Bobrovsky, who is not expected to be brought back, Toronto Maple Leafs' Jonas Gustavsson, Minnesota Wild's Josh Harding, Florida Panthers' Scott Clemmensen and the New York Rangers' Martin Biron.