It was confirmed on Saturday that Stoddart sustained a fracture to a bone in his hand and the player will now be monitored daily to assess his progress.
"Morgan has been given a window of opportunity," said Wales physiotherapist Mark Davies.
"If his symptoms settle down we will clear him to play subject to a fitness review later in the week."
Blues wing Chris Czekaj has been called into the squad to cover for Stoddart. Meanwhile, Wasps No8 Andy Powell has been ruled out of the clash with the Scots after injuring the A/C joint in his shoulder in the first half of the defeat to England last Friday night.
"Andy needs a period of rest now, but if all goes well he should be back in contention for the Italy game at the end of the month," added Davies.
Blues wing Leigh Halfpenny is the only other player on Wales' injury list, he is recovering well after spraining an ankle in training in the lead up to the England match and is also targeting a return against Italy.
National Squad Commmunications Manager
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