The Calgary-based company announced a formal review on Thursday, and said options included a possible "corporate transaction."
Infrastructure company Brookfield had offered C$16.50 per share for Inter and said it was willing to go as high as C$18.25 if the pipeline operator gave it access to due diligence.
At the top price, Brookfield's offer valued Inter at C$7.8 billion ($6.15 billion) but the pipeline company rejected the offer, saying it was too low.
On a conference call on Friday, held to discuss Inter's quarterly earnings, Chief executive Christian Bayle made it clear the board would consider an acquisition by Brookfield as part of the review process.
"The intention is to evaluate a broad range of corporate options, one of which obviously is a possible corporate transaction. I think it's fair to say the board would not preclude including Brookfield in that process if they would participate," Bayle said.
"No timetable has been set and no decisions have been made regarding strategic alternatives."
(Reporting by Nia Williams; editing by Jonathan Oatis; Editing by Chris Reese)
By Nia Williams