Adkins was dismissed with the Addicks in the bottom three of League One after 13 matches and his former assistant Jackson will take charge of Saturday’s visit to Sunderland.
Sandgaard revealed Jackson, 39, would have a chance to earn the job, although confirmed he would also consider appointing another coach from outside the club.
“Absolutely. That’s the goal – that he gets a chance to work towards the job permanently,” the Dane told Standard Sport.
“He obviously has a lot of experience and did a good job as an assistant manager. We’re definitely going to give him a good chance to work it out for the team.
“Of course we’ll still be looking at anything that can put us in a stronger position from the outside. We have the existing structure of Johnnie being assistant manager and Jason Euell being the assistant coach, so that’s something we can look at keeping in place too.”
Sandgaard added that he still hopes Charlton can reach the League One play-offs this season and revealed he would take a “more hands-on” approach to running “the football side” of the club after their difficult start to the campaign.
Adkins succeeded Lee Bowyer on a two-and-a-half year deal in March and was tasked with beginning to realise Sandgaard’s grand vision of returning the club to the Premier League and European football within a decade.
But with promotion to the Championship the target for this season, the Addicks have won just two of their opening 13 matches and Sandgaard decided to act following back-to-back defeats to Lincoln and Accrington Stanley this month.
Jackson spent eight years as a Charlton player and has been on the coaching staff since 2016, having previously been Bowyer’s assistant manager.
He took charge of one game as caretaker in early March, a 3-2 win over Bristol Rovers at the Valley, and will be assisted by another former Charlton player in Jason Euell.