Hoops manager Mowbray has already brought in Ki Sung-Yueng from FC Seoul, Jos Hooiveld from AIK Solna and 19-year-old Thomas Rogne on freedom of contract from Norwegian side Stabaek during this transfer window.
Mowbray, who revealed Rasmussen is likely to make his debut in Wednesday's SPL clash against Hibernian at Parkhead, hinted at more to come.
"I sit here happy that we have a balance of strikers that can get the job done," he said.
"Morten's a different type of striker to the ones that we have got.
"Hopefully, given the opportunity, he can score goals which will obviously help the team."
"I am just trying to shape a team and you only get two opportunities to do it.
"I could sit on my hands and do nothing or I can get started.
"I don't think any manager is ever totally settled and happy.
"You are constantly trying to add and improve to increase competition in all areas of the pitch.
"If good players become available then it is very unlikely that we will turn them down.
"We are working very hard to do that (add more) but it is never easy; there are a lot of parts to come together."
Rasmussen, nicknamed 'Duncan' after former Rangers and Everton striker Duncan Ferguson, is ready to show Hoops fans what he can do against Hibs.
"I played two matches last week with the national team so I feel ready," he said.
"I am a box player, I like to be in the box and that's where I score most of my goals.
"I will give all I can and hopefully that is good enough."
Kevin McBride reckons Hibs risk the same fate as St Johnstone if they fail to keep 11 men on the field tonight.
Saints led Celtic in Sunday's game at McDiarmid Park until Graham Gartland's sending-off sparked a 4-1 rout.
"They went down to 10 men at their home ground and pretty much got battered," said Hibs midfielder McBride.
"It'll be an even more difficult task at Parkhead if we go down to 10 men.
"The manager's said to us we've got to keep 11 men on the pitch."
McBride's first start since November coincided with Saturday's 5-1 thrashing of Hamilton, Hibs' first win in four SPL games.
He added of Wednesday's match: "We've got to go there with a lot of confidence after our game on Saturday.
"We got back to winning ways."
McBride believes both sides will be wary of the other's attacking threat, with Celtic boasting the likes of Aiden McGeady and Paddy McCourt, and Hibs able to unleash Derek Riordan, Anthony Stokes and Colin Nish.
"That's the difficult thing, playing against these players, like McGeady, McCourt, who can change the game in a second," McBride said.
"They've got two strikers as well who can score at any time in the game.
"We've got strikers who can do the same.
"When we come up against teams - even the Old Firm - they'll look at the strikeforce we've got, with Derek, Stokesy, Nishy."
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