AutoCAD definitely can import MicroStation DGN design drawings and export it in a universal exchange DXF format.
Convert MicroStation drawing to AutoCAD DXF Drawing Exchange Format.
We found 4 software records in the database related to .dgn to .dxf file format conversion.
Microsoft Windows software - convert dgn to dxf on Windows
Leading 2D and 3D CAD development software from Autodesk
Convert from dgn file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned dgn to dxf. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
A feature rich 3D CAD software by Siemens
A simple DGN to DWG converter
A 3D CAD translation softwate