Elwood does hope to have Parks available for the start of his side's Heineken Cup campaign against Zebre on October 13 and he may play some part against Connacht's two preceding fixtures, including this Friday's clash with Leinster.
But Elwood believes that in Parks' absence, out-halves Matthew Jarvis and Miah Nikora have performed admirably.
"We are taking Dan week-on-week," Elwood told the Irish Independent. "Part of his rehab is to get some conditioning work under his belt.
"This is a very important week for Dan and some of those injured guys, because if we can get some of those conditioning hits into them this week, then they can put their hands up for selection next week. Hopefully they can get through the workload.
"We brought in lads last week and they performed. It is a long season."
63x46.png){kind=logo}