The 29-year-old, who has not been named, was initially taken into custody earlier this month over an alleged attack in June.
He was then questioned over two further rape allegations against a different woman, one in April 2021 and one in June 2021.
The Metropolitan Police said on Thursday no further action will be taken over the June 2021 allegation but investigations continue into the other allegations.
His bail has now been extended to October.
In a statement the Met Police said: "No further action will be taken in relation to the offence in June 2021 but the investigation into the remaining offences is ongoing.
"The man was initially bailed until a date in August but his bail has since been extended to a date in early October."
On 13 July his club said the player, who denies the allegations, would not be suspended.
"We are aware of the allegations which are currently the subject of a police investigation," said the club, which has also not been named, in a statement at the time.
-- Courtesy of BBC Sport