The pair have both been handed regular action this season, with Leighton Baines and Seamus Coleman out injured, and they have excelled.
Both Browning and Galloway have been key as Everton have put together an impressive opening to the season and they coped admirably in the Merseyside derby against Liverpool at the weekend.
And Le Tisser said: "I've been impressed by the two full-backs, Browning and Galloway. The pair of them were very good [against Swansea City]. They've come in and replaced some very experienced and talented full-backs [in Leighton Baines and Seamus Coleman], but they've not looked out of place."
Everton have produced some very talented youngsters in recent times, and it seems that Browning and Galloway could be the next ones off the production line.
With Ross Barkley becoming a key player for the Toffees and John Stones, who was brought from Barnsley, also establishing his place in the back-four, there is proof that Roberto Martinez will trust his youngsters, if they prove that they can cope with the step-up.
So far Browning and Galloway have done just that and Coleman and Baines both will face fights to win their places back in the team, when they do return to fitness.
Everton are currently in seventh place in the Premier League table, and they face Manchester United at Goodison Park when the international break finishes.