Johnson, 47, left Sean Holley and Jonathan Humphreys in charge of first-team affairs for the 27-19 win following the health scare.
But the Australian hopes to return and watch the tie in San Sebastian from the stands.
Ospreys head coach Holley said: "Scott is on the mend but he has had some health issues. He is not 100 per cent but he is back in work and taking small steps.
"It will be very difficult to stop him from travelling."
The Ospreys travel to northern Spain for the mammoth last-eight clash this Saturday boosted by the return to fitness of British Lions Shane Williams and Alun Wyn Jones.
Williams and Jones came through unscathed from the narrow victory over their west Wales neighbours following shoulder and elbow injuries.
And Holley confirmed the star Wales duo will be involved in their 23-man squad to face the French giants.
Holley added: "It's good news for us. Shane and Alun are back quicker than we imagined.
"It was good to get them back on the field for 20-25 minutes but selection will be really tough."