The Black Cats took the opportunity to travel to Dubai for some warm weather training last week as they were not involved in the FA Cup fifth round, and O'Neill was able to try out some new combinations.
Graham, who joined Sunderland from Swansea on transfer deadline day, has featured on the bench in the defeats by Reading and Arsenal, but could be included in O'Neill's starting XI for the trip to The Hawthorns.
Steven Fletcher has played mostly as a lone striker since his arrival at the club last summer, but the Black Cats manager could shake that up if Graham makes the grade.
O'Neill said: "(The trip to Dubai) gave Danny an opportunity to work with the players he hasn't done before.
"We took ourselves away for a few days and the weather was really fine and gave us a chance to do a bit of training in the sun. I hope it works out well.
"In time he (Graham) will play. He might even start the game on Saturday but it is really about Danny integrating with the team.
"He's a very good player and he has played at other clubs and it hasn't taken him too long to settle down at certain places.
"Like anything else, of course he would like to get on and score and get himself settled down - and all of those things will happen."
Sunderland are only competing on one front, to secure their place in the Barclays Premier League for next season.
O'Neill, a staunch advocate of a winter break, believes a change of scenery and some time away from the cold weather in the north-east could work wonders.
The former Celtic boss said: "I suppose eventually, the next 12 games will decide if it is a good idea or not.
"Personally speaking, I'm a great advocate of a winter break anyway and during my time in Scotland I felt how beneficial that was - and I don't think it will do us any harm.
"We were able to train early enough in the morning before the sun got really warm and it was very good. It was worthwhile.
"We really had a stop-start pre-season. Within two days we were off on a trip to South Korea which had been organised beforehand and some players were coming back from international duty with the European Championships, so it was almost like a mini pre-season for us."
Sunderland are currently in 13th place in the Premier League standings with 29 points, six above Reading who occupy the highest relegation spot.
However, with only two league wins under his belt this year, O'Neill knows his side will need to remain fully focused from now until May.
"Any side in the bottom half of the table has got to be looking over their shoulder. I think that is the case and it is too close to call," the Black Cats manager said.
"I've also said it's points on the board rather than position in the table which is really important.
"Certainly it will be more important in the last few games of the season and there are many points to still play for. It's really up to us now to do something about it."
Sunderland have a couple of injury worries ahead of the match, with on-loan Tottenham defender Danny Rose missing out with a hamstring injury he aggravated in the 1-0 defeat by Arsenal while midfielder Lee Cattermole is a doubt after he only managed 45 minutes in that match after returning from a knee problem.
O'Neill said: "We have got a few injuries still despite the fact we haven't played for a fortnight and we have still got a few players who will be missing from the game on Saturday.
"That said, we are a Premier League side, therefore we should be able to cope with these things.
"Danny Rose came with us on the trip (to Dubai) but he would be very doubtful, in fact he would have no chance of playing against West Brom."
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