Absolutely do not do this! Vertical blinds need a support every 3 foot as a minimum. One way blinds need extra support on the stack end, where they are when opened.the extremities only.
Vertical blinds are heavy.
Most door units are vinyl now and mounting to the space between is not secure enough. It may well damage the door and or hurt people when it falls.
If the transom and the door are separate units and there is framed structure between the 2 then it would be okay. Ask the builder.
Otherwise you have no choice other than to go over the transom on the wall and into structure.