The duo impressed during their six-month spells at Tynecastle this term and have been linked with a return to Edinburgh.
Manager Craig Levein has made no secret of his desire to keep hold of Mitchell and Naismith - on loan from Manchester United and Norwich respectively - and Budge says the club are trying to get deals done.
“We would like to secure their services again, but to a large extent it is out of our hands,” she said.
“We have made it known that we would like them and they have made it known they would like to stay here so if the other clubs involved see it that way too, then I am reasonably optimistic.”
Budge was speaking after it was announced that fan group Foundation of Hearts had fulfilled their promise of a £3 million contribution to the Tynecastle Redevelopment Fun, which went towards the construction of the new main stand at the ground.
Pledges from the fan group will now go back to majority shareholder Budge’s company BidCo - with the aim of becoming the biggest fan-owned club in Britain - and will enable Levein to put more money into his playing squad.
Budge insisted the club would not go overboard with investment just yet: “We are still building the team as well as the stadium,” she said.
“By this time next year I would like to think the bulk of this (building work) will be finished, and then we are simply looking at what we need as a football club, rather than a construction project.
“Moving forward we will still have to run it (the club) as a business, and I would always stress that is a priority, but there will hopefully be more funds available.”
The club was forced to play away from their home until November 19 due to the ongoing building work at the stadium, which, along with the early sacking of Ian Cathro, resulted in a turbulent start to the season.
The appointment of Levein helped them secure sixth in the Ladbrokes Premiership, but Budge wants better next campaign.
She said: “The league is in a very good position. There are a lot of teams doing very well and it’s very competitive, but we want to be up there in the top three or four clubs in Scotland, higher if we can.
“Our ambitions won’t change; we want to be playing in Europe which means we have to finish third or fourth and we want to have a better cup run next year.”