The 29-year-old scored a last-gasp drop goal in Edinburgh's crucial 27-24 Heineken Cup victory over Racing Metro on Friday and will be looking to take full advantage of Jackson's enforced layoff.
The Glasgow Warriors fly-half injured his thigh when kicking a first-half penalty in the 16-14 defeat to Scarlets on Saturday but Godman is just glad to be back playing.
"You always think about getting back into it for the club but also about playing for Scotland as well," said Godman, who has won 23 international caps.
"It's just great to be back playing for Edinburgh and to be back involved with Scotland."