"Muliaina returned to Galway on Sunday April 5th, having cooperated fully with police investigations," media spokeswoman Louise Creedon said.
"He denies any wrong doing and will meet with Connacht Rugby officials in the coming days to review the situation internally".
She said the club could not comment further as it remained a legal matter.
Earlier in the day, New Zealand Rugby Players Association chief executive Rob Nichol said it was "completely appropriate" that Muliaina continued to train with his team.
"Mils has got nothing to hide, he has denied all wrongdoing and he has been fully co-operative," Mr Nichol said. "Why would you then punish him by suspending him from work? I don't think it is to anyone's advantage."
Mr Nichol said a player would only be stood down if allegations were so severe it was not "practical or sensible" for them to continue with their job.
"Sometimes things can be that severe that you can take that approach but not in this instance with Mils. Absolutely not," he said.
On Monday, Mr Porter said Muliaina wanted to get back on the field with his teammates.
"He is looking forward to getting back into training with his team and will just have to wait for the police to get back in touch when they have completed their investigation."
Speaking to Radio New Zealand yesterday morning, journalist Ruaidhri O'Connor of the Irish Independent said not a "huge amount" was known about Connacht Rugby's internal investigation into allegations made against Muliaina.
"Connacht are looking at next steps rather than anything beyond that. They will look into the incident of course but as it stands Mils Muliaina has not been charged with anything."
Mr O'Connor said Muliaina had been taken off the field due to an injury before he was arrested on Friday, and it was unknown whether Muliaina would play for Connacht again once his injury healed.
"He's back training with them at the moment so we are just waiting to see how they are going to proceed from there.
"If there are no charges brought I don't see any reason why they wouldn't, although there is obviously a cloud hanging over him," he told RNZ.
"He hasn't played particularly well since he arrived in Ireland ... There is a younger Irish rival to his position. It might suit Connacht to kind of take him out of the equation.
"He's leaving the club at the end of the season anyway so it might be time for them to go with the players who will be there next season."
Connacht Rugby had scheduled a press conference for today, he said.
Muliaina was taken in for questioning after his arrest at the weekend.
When police picked him up after his team's 14-7 defeat to Gloucester in the Challenge Cup on Saturday, the fullback believed he was being collected for drug testing.
Police have not said what date the alleged incident occurred, however Connacht played the Cardiff Blues in the city on March 6.
Muliaina, who has agreed to return to Cardiff for questioning in July, has not been charged and was released on police bail.
A spokesman from Italian club Zebre, which has contracted Muliaina for next season, said it was aware of the allegation, but had no comment.
Busker Brownes, the Galway pub which sponsors him as a Connacht player, said on Monday it had no comment to make on the matter. When asked whether the pub would withdraw sponsorship, it again refused to comment.
