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.

His side beat Cheshire on Sunday to retain the title they won last year.
However, with crowds at the final falling, there is speculation that the Rugby Football Union could take the game to a smaller ground in future.
"Hopefully they don't take it away from the stadium, because young players want to play at this stadium," said Dawe.
"It all depends on the RFU, doesn't it? How they keep this competition going, how they keep it alive."
Cornwall have now reached the showpiece game in each of the last four years.
The final of the competition, also known as the Bill Beaumont Cup, has been played at Twickenham since 1984.
"It is a problem, it's not perfect by any stretch of the imagination," Dawe added to BBC Sport.
"All you can do is the best with what you're dealt and don't look at it too gloomily, but who knows what the future holds."

Victoria Street in Victoria flooded at about 18:00 BST on Saturday and the water gushed into several businesses including the Curzon Cinema, which had to be evacuated.
Fire crews then helped some people in the venue cross the flooded pavement.
Thames Water said a large pipe burst damaging the road but no customers were without water on Sunday.
A spokesman for the company said: "Our team is on site arranging emergency repairs.
"We apologise for any inconvenience caused and we will fix the pipe as soon as possible."
The road remained closed between Palace Street and Buckingham Gate on Sunday morning and several buses in the busy area were on diversion.
On its website Curzon Cinemas Victoria said: "Due to a burst water main, Curzon Victoria has had to close tonight (Saturday 6th June).
"We apologise for any inconvenience caused."
Glamorgan have made signing another fast bowler their priority for 2017, says chief executive Hugh Morris.
[NEXT_CONCEPT]
Cornwall coach Graham Dawe hopes the County Championship final is not moved from Twickenham as part of a potential revamp of the competition.
[NEXT_CONCEPT]
Cinema-goers were carried to safety by firefighters after they became stranded when a water main burst in London.