Brady enjoyed a memorable debut for the Republic of Ireland, scoring one goal and setting up two more as Giovanni Trapattoni's men strolled to a 4-1 friendly win over Oman at Craven Cottage
"I want to stay playing [for Ireland]. I don't want to come in and doss about so I need to be playing as many club games as I can," Brady said.
"If that means I need to take a loan move, I will. We'll see what happens.
"I'd just like to play as much football as I can and hopefully I can push on and keep playing (for the national side)."
The 20-year-old's cross set up Shane Long for the opener on Tuesday night and he then lashed in their second before curling in a world-class cross that Kevin Doyle nodded home after 36 minutes.
Brady last year had a successful loan spell at Hull but is yet to make his first-team debut for Sir Alex Ferguson's side despite going on the club's pre-season tour of South Africa.