I'm from South Asia and we speak in a way directly translated from our language structure so often. If I'm making some request "I'm partnering with Elsa for group discussion right now, let's say I wanted to show her my progress would you like to accompany me to her house?". Is there anything wrong with the sentence especially "..let's say I wanted.." or it should be "..let's say I want.." instead. Thank you
I think that both uses are fine.
For the most part they mean the same thing, although they could be used to mean slightly different things.
Let's say I wanted . . .
This is being used as a hypothetical. I would use it if I were considering one or another action:
Let's say I wanted to go to the ball—should I wear a regular tie or a bow tie?
If I go to the ball, should I wear a regular tie or a bow tie?
As for the other:
Let's say I want . . .
I would not take this in quite the same hypothetical fashion, but as an assertion.
Let's say I want steak for dinner. I like mine medium rare.
Go ahead and assume I want steak for dinner. I like mine medium rare.
This distinction can be emphasized with the word just:
Let's just say I want steak for dinner.
This sounds normal along with the assertion.
Let's just say I wanted to go to the ball.
This, however, sounds a bit awkward because just isn't normally used in association with a hypothetical.
If I continue this with your example, I might make a slight modification to your phrasing, depending on the use of wanted or want:
Let's say I wanted to show her my progress. Would you  accompany me to her house?
Let's (just) say I want to show her my progress. Would you like to accompany me to her house?
In the first, as a hypothetical, I dropped the like to because it seems more natural to be asking for a simple consequence. (If I show her my progress, will you accompany me?)
Meanwhile, in the second, showing her my progress is assumed. (Let's assume that I'm showing her my progress. Would you like to accompany me?)
But there is no reason to assume that this distinction will be picked up on and understood. For practical purposes, you can use either let's say I wanted or let's say I want without any difficulty.
Update: It was suggested in a comment that I provide an explanation as to why the different verb forms could lead to different meanings.
Here, let's say I want is in the present tense. When something is in the present tense, it has an immediacy and is used to describe an actual situation.
Meanwhile, let's say I wanted is in the past tense. (Forget for the moment that when used in the hypothetical sense I've described it's actually postulating a future event.) Any verb form that isn't in the present is distanced from it and, therefore, less immediate.
Hypothetical situations are, by their nature, more easily understood when distanced from the present.
So, the present tense here is more suited to an assertion of fact, while the past tense is more suited to the expression of a hypothetical situation.
Is this what you want to say?
"I'm with Elsa in a group discussion right now, and we might discuss my progress with the project at her house later today. Would you like to accompany me to her house?"
I am guessing this is what you meant, but I could be wrong.