We are renovating our basement. There are 2 I-Beams, approximately 10 feet apart, running the length of the house, perpendicular to the floor joists. The shorter beam is supported by 1 post and the other beam is supported by 2 posts. There is a wall, about 1 foot from the shorter beam, running parallel to it about 2/3 of the distance of the basement. We are wanng to remove this wall and open up the space. Would it be safe to do so, or is it possible this wall could be load-bearing in any way?

Its really impossible to guess for sure either way without actually being able to see it in person looking for indications its load bearing. But with the consequences that would occur if it was load bearing I'd pay a qualified contractor to visually acess if it is or isn't a load bearing wall before you proceed.

dont do it it isnt a risk i would be willing to take. You should get some advise from a proffesional builder that way your taking a safe risk.

A picture would really help but I'd say your load is carried by the beams and posts and not the wall. If you open the wall and find it to be single 2x4 studs they are not carrying any load. You could also go to your building department and ask them to check the old blueprints to be sure