Mjallby today said there had been no fresh bids for Hooper since Norwich had an offer rejected late last week.
Hooper brushed aside the speculation over his future by scoring twice in a 4-1 victory over Hearts on Saturday and is preparing to face Dundee United in a rearranged Clydesdale Bank Premier League fixture tomorrow.
Mjallby said: "The situation hasn't changed at all since Saturday. We don't want Gary Hooper to leave. I think he is very happy here. He put in a great performance the other day.
"He is enjoying his football, he is enjoying playing for Celtic and enjoying his team-mates.
"Not only his goals at the weekend, but his general performance was very, very good.
"The only bid has been from Norwich but we expect there are going to be offers for our best players anyway. That's the way it is in this climate."
Mjallby confirmed reports that 6ft 2in Austin is a potential target should Celtic need a new forward.
The 23-year-old, who cost Burnley a reported £1.8million from Swindon in July 2011, has scored 23 goals this season after netting 17 last term.
"He might be on the shortlist," Mjallby said. "Charlie is a proven goalscorer and he might come in handy in the future.
"But right now we think Gary will stay on, at least until the summer, and that will be great for the club.
"He is a top-class player. It's not only his goals, the last couple of months have shown he is improving his all-round game.
"We can use him in midfield as well because he is a very clever player.
"We want to keep him because he is improving and making the team better.
"Gary has proven to be the best goalscorer for us so that's one of the reasons we want to keep him.
"We always have a shortlist for players in each and every position but right now we are just thinking about Gary staying because he is a very important figure for our squad."
Mjallby, who dismissed reports that Yokohama Marinos forward Yuji Ono was a serious target, is braced for further bids for Hooper and other players.
"I'm sure there will be bids for a lot of players here in the summer but if that happens it's up to the board, the manager and the chief executive to discuss that," he said.
"Even if you get a lot of money for Gary, if a bid comes in and the board and everyone thinks it's good enough, it's always a gamble because money doesn't always buy you a good player.
"Right now we know what we have got, we have a good squad and players we know and how they function.
"If you buy a new striker, you never know if it's going to be successful or not."
Celtic are again set to be without goalkeeper Fraser Forster against United but his injury appears to be minor.
"Fraser has a stiff back/neck," Mjallby said. "It's more of a precaution to make sure he is going to be 100 per cent for the coming games.
"So he is going to be a doubt to start tomorrow. We have done a scan and it didn't really show much. It's no worries when it comes to his health.
"We just want to make sure, because he is such an important player for us, that he is going to be 100 per cent fit in February."
United travel to Celtic Park on the back of an impressive 3-2 victory at Kilmarnock and Mjallby is looking for a repeat display from his team following their emphatic win over Hearts.
"Usually when we play them they are very competitive and tight games," he said.
"They have got plenty of good players that can hurt you so we need to be at our best.
"But it was very encouraging to see how the team performed at the weekend and hopefully we do the same tomorrow and it will be hard for Dundee United."