First things first. Is this a wood joist construction or is this over a concrete slab? Believe it or not, this is a VERY important bit of info.

Excellent. You MUST run the wood floor perpendicular to the JOISTS. You have NO CHOICE. Perpendicular simply means the wood plank will run across the joist.

And now you have to have someone assess the DEFLECTION RATING of the wood/joist system and it's ability to accept tile. Tile deflection ratings are VERY specific. If your subfloor is too thin or the joists too far apart then tile installs become complicated. You need a STIFF subfloor to accept tile. Tile is SUPER heavy and it does NOT like "movement" from a flimsy construction subfloor.

That being said and we ASSUME you have a STIFF enough subfloor, it is no big deal to throw down tile. The wood install can be altered IF you add MORE thickness to the subfloor. If you add another 3/4" of plywood to what is already there, you can go in any direction you choose. That's expensive but it is how we get around the "joist" direction problem.

The *other way around the joist direction problem is a DIAGONAL installation of the wood. That gets very expensive for two reasons:

1. You need MUCH MORE wood floor waste (15% - 25% waste for diagonal install; compare that to 5% waste for a traditional install)

2. Labor costs are MUCH more to lay diagonally. There are a tremendous amount of cuts which means the installer could need DOUBLE the time.

And time is money. Some of these guys charge $50/hour. If you DOUBLE the TIME you DOUBLE the labor costs.

Personally I believe laying another layer of plywood is a better/cheaper/faster option if you MUST change the direction of the wood.

Again...the traditional/required install is perpendicular to the joists. Everything else becomes a personal choice...with personal financing required.