A public back and forth has played out between the pair since Cahill opted to stay in China in February.
Gallop had said he was told there was no way A-League clubs could meet Cahill's needs, a claim refuted by the player.
Australia's all-time leading goalscorer is in the final months of his Hangzhou Greentown deal, leading to further suggestions he may move to the A-League.
In a statement on Wednesday, Gallop said he met with Cahill – who insisted he would always remain open to playing in Australia's domestic competition.
"I'd love to see him playing every week here," Gallop said.
"We are ready to explore the opportunity of him playing in the A-League, including looking at the off-the-field activities that Tim is so passionate about including his academy program and other grassroots initiatives.
"I obviously regret that my comments in February were taken as a criticism of him and the whole thing became the subject of so much commentary.
"The relevant issues around his decision to stay in China could have been more clearly explained by me.
"With his kids only just starting new schools in Shanghai, the option of playing at Hangzhou Greentown was the best next move for him.
"Tim indicated this to senior FFA people and me personally in the hours after he parted company with Shanghai Shenhua.
"Our communication on that particular day was via text messaging.
"Bottom line is Tim would be a massive addition to the A-League. I would love to see him playing here every week."