Timm van der Gugten, Michael Hogan, Graham Wagg and Craig Meschede took on the bulk of the fast bowling duties across all three formats in 2016.
Van der Gugten was the leading wicket-taker with a haul of 82.
"You can never have enough good fast bowlers, so that would be top of the shopping list," Morris said.
"If we can find some money in the bank, we need to supplement our fast bowling department, of that there's no doubt.
"Timm van der Gugten proved what an excellent cricketer he is. He was a really good addition."
Australia-born Netherlands international Van der Gugten joined Glamorgan before the 2016 season.
Teenager Lukas Carey topped the Championship averages with 13 wickets in three games, but Ruaidhri Smith was limited to one match by university commitments and injury.
The county hope that leading batsmen Colin Ingram and Chris Cooke will be fit to resolve their batting problems after long-standing injuries.
Ingram is hoping for a comeback in South Africa by November after a knee operation on the problem that restricted him to limited-overs cricket in 2016.
Cooke is due to step up training in late October 2016 after being laid low by a back problem in May, although he was advised against surgery.
"There's no doubt they left a big hole in our side this year, two of our most experienced and best batters," admitted Morris.
He is also hoping for a bigger contribution from captain Jacques Rudolph, who managed just 659 Championship runs.
"Jacques had a really disappointing summer, he's been a professional cricketer for 19 years and this was his most challenging summer," Morris added.
"But I know what a proud man he is and a good player and he's determined to turn that round."
Morris says a record of three wins and eight losses in the Championship was disappointing, but points to the progress made by younger players.
Aneurin Donald, David Lloyd, Nick Selman, Owen Morgan and Kiran Carlson all hit maiden Championship 100s in 2016.
Glamorgan have made signing another fast bowler their priority for 2017, says chief executive Hugh Morris.