It is thought Rooney, 32, is willing to leave his boyhood club Everton, one season after returning to the club.
No announcement on Rooney's future will be made until July 10, when the MLS transfer window opens, but it would be no surprise if he chose to follow a trail favoured by ageing pros.
"My understanding of the situation is there seems to have been some negotiation somewhere along the line", said Allardyce ahead of his side's trip to West Ham. As to clarity of whether Wayne is leaving or staying I'll find out when he comes in for training today.
"We still, I think, need another goalscorer that gets 15 or more goals in the Premier League next season".
Wayne himself looks set for a new chapter in his footballing career with reports linking him with a move to the MLS and DC United are said to be the closest to his signature.
Rooney's agent Paul Stretford is said to have been in the US with talks at an advanced stage between the player's representative and the Major League Soccer (MLS) outfit.
When first asked about the deal, Olson told reporters in the USA: "I don't know what you're talking about".
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Although Rooney remains Everton's leading goal-getter this season with 11, he last scored in December.
Allardyce clarified that his stance on players who wish to move did not apply only to Rooney.
"If you watch Lionel Messi play football in a live game you can not believe how many times he stands still in a football match".
In this picture, Wayne Rooney of Everton reacts during the Premier League match between Everton and Newcastle United at Goodison Park on April 23, 2018, in Liverpool, England. If the player wants to leave - if any player does - I'm comfortable with it.
The Englishman is well loved by the club's supporters but his class doesn't impress many others who perhaps don't watch him on a regular basis.
"The next level of recruitment has to be quality players to get into the team and make them better than what they are at this moment in time. They did then, I don't know if they exist as much now".
As for whether uncertainty about his future at the club might affect his planning for next season, Allardyce replied: "I've already done it".