Gibbs has been sidelined with an ankle problem, while Wilshere has been out for almost two months after a foot injury sustained during England's friendly against Denmark.
Wenger indicated the duo are likely to feature in the FA Cup final later this month but stressed the team's focus is on ending their 2013/2014 Premier League home campaign in style.
"Kieran Gibbs is very very close now (to returning from injury) and Jack Wilshere is not far away as well," the Arsenal manager said. "They are both very close to being integrated back into training again.
"We have to finish as close as possible to the top and to win our remaining games - that is what is at stake for us.
"The important thing for us is the next game. Let's win at home to West Brom. It is our last home game. The FA Cup is two weeks away. That is a long time."
Arsenal have suffered just one Premier League home defeat all season and that came on the opening day against Aston Villa, who beat Wenger's side 3-1.
Wenger admitted his side have improved since then and believes they would have been much closer to the top had they converted some of their home draws into wins.
"We started in the worst possible way and after some rest we've had a good strong home record," he said.
"The only restriction has been maybe that in the big games we had a few too many draws and not won some of them. That is maybe where the missing points are at the moment because we are very close to the top and one or two more wins at home could maybe have made that difference.
"When we came out of Christmas, we were in a strong position and what you want then is to have your strong players available in March and April. We had too many injuries.
"It is very, very difficult - you can have one or two, but after that when you have too many injuries you always have to play the same players and that is detrimental to the efficiency of the group.
"The regret we have is that too many players were out at the same time between Christmas and April."