Baines has missed most of the season so far with injury, but he has come on as a substitute in Everton’s last two matches against Middlesbrough and Crystal Palace.
Although the 31-year-old is not ready to play 90 minutes just yet, Martinez is optimistic that the England international will be back to full fitness soon.
"After the Middlesbrough game he took a little bit of a knock and it took him probably 24 hours to get back to normal," he said. "After the game against Crystal Palace, he had no reaction.
"We need to be very much aware when a player's out for such a long period, you cannot just expect to come back and be perfect for 90 minutes.
"But I was delighted with the way he reacted after the game on Monday. He's getting very, very close to being able to challenge for a start."
Everton’s need to rush Baines back to health has been reduced due to the form of Brendan Galloway in his absence.
The youngster has been superb in his showings for the Toffees this season, and his eye-catching displays have helped to earn a new contract until 2020.
Galloway is, therefore, likely to start for the Toffees against Norwich City on Saturday, with Baines coming on as his replacement late on.
If Everton can beat Norwich they could move up to sixth in the Premier League table, which would represent significant progress from last term.