Thomson was sent off during Sunday's Co-operative Insurance Cup final win over St Mirren, but if boss Walter Smith appeals, the Scotland midfielder could be eligible to play at Tannadice.
And, with Scottish Football Association rules dictating that Rangers can appeal up to three days after the match, they could lodge the papers hours before the Tannadice kick-off.
Houston said: "If I was in the same situation I might well use it (the appeals procedure). The rules are there to be used.
"If they appeal it then they obviously think they've got a good chance. They're just using what has been put in place by the SFA so we'll have to wait and see."