UIImageView get the position of the showing Image

I recommend using built in function AVMakeRectWithAspectRatio.

func AVMakeRectWithAspectRatioInsideRect(_ aspectRatio: CGSize, _ boundingRect: CGRect) -> CGRect

Parameters:

aspectRatio:
The width and height ratio (aspect ratio) you want to maintain.

boundingRect: The bounding rectangle you want to fit into.

Return Value Returns a scaled CGRect that maintains the aspect ratio specified by aspectRatio that fits within bounding Rect.

let boundingBox = AVMakeRectWithAspectRatioInsideRect(backgroundImage.size, frame)

Swift 4.2 & 5.0

func calculateRectOfImageInImageView(imageView: UIImageView) -> CGRect {
        let imageViewSize = imageView.frame.size
        let imgSize = imageView.image?.size

        guard let imageSize = imgSize else {
            return CGRect.zero
        }

        let scaleWidth = imageViewSize.width / imageSize.width
        let scaleHeight = imageViewSize.height / imageSize.height
        let aspect = fmin(scaleWidth, scaleHeight)

        var imageRect = CGRect(x: 0, y: 0, width: imageSize.width * aspect, height: imageSize.height * aspect)
        // Center image
        imageRect.origin.x = (imageViewSize.width - imageRect.size.width) / 2
        imageRect.origin.y = (imageViewSize.height - imageRect.size.height) / 2

        // Add imageView offset
        imageRect.origin.x += imageView.frame.origin.x
        imageRect.origin.y += imageView.frame.origin.y

        return imageRect
    }

Swift 3.0

// MARK: - Create Rect
func calculateRectOfImageInImageView(imageView: UIImageView) -> CGRect {
    let imageViewSize = imageView.frame.size
    let imgSize = imageView.image?.size

    guard let imageSize = imgSize, imgSize != nil else {
        return CGRect.zero
    }

    let scaleWidth = imageViewSize.width / imageSize.width
    let scaleHeight = imageViewSize.height / imageSize.height
    let aspect = fmin(scaleWidth, scaleHeight)

    var imageRect = CGRect(x: 0, y: 0, width: imageSize.width * aspect, height: imageSize.height * aspect)
    // Center image
    imageRect.origin.x = (imageViewSize.width - imageRect.size.width) / 2
    imageRect.origin.y = (imageViewSize.height - imageRect.size.height) / 2

    // Add imageView offset
    imageRect.origin.x += imageView.frame.origin.x
    imageRect.origin.y += imageView.frame.origin.y

    return imageRect
}

For Swift < 3.0

Here is the above method in Swift. Again, assuming that contentMode is set to .ScaleAspectFit If there is no image on the given imageView CGRectZero will be returned.

func calculateRectOfImageInImageView(imageView: UIImageView) -> CGRect {
    let imageViewSize = imageView.frame.size
    let imgSize = imageView.image?.size

    guard let imageSize = imgSize where imgSize != nil else {
        return CGRectZero
    }

    let scaleWidth = imageViewSize.width / imageSize.width
    let scaleHeight = imageViewSize.height / imageSize.height
    let aspect = fmin(scaleWidth, scaleHeight)

    var imageRect = CGRect(x: 0, y: 0, width: imageSize.width * aspect, height: imageSize.height * aspect)
    // Center image 
    imageRect.origin.x = (imageViewSize.width - imageRect.size.width) / 2
    imageRect.origin.y = (imageViewSize.height - imageRect.size.height) / 2

    // Add imageView offset
    imageRect.origin.x += imageView.frame.origin.x
    imageRect.origin.y += imageView.frame.origin.y

    return imageRect
}

The following will answer your question, assuming your UIImageView used UIViewContentModeAspectFit:

You have to regard the image sizing of the image inside UIImageView. This depends on how you set the contentMode. According your description, I assume you are using UIViewContentModeAspectFit. The resulting image will also be centered in the UIImageView so you also have to consider this for the calculation.

-(CGRect )calculateClientRectOfImageInUIImageView:(UIImageView *)imgView
{
    CGSize imgViewSize=imgView.frame.size;                  // Size of UIImageView
    CGSize imgSize=imgView.image.size;                      // Size of the image, currently displayed

    // Calculate the aspect, assuming imgView.contentMode==UIViewContentModeScaleAspectFit

    CGFloat scaleW = imgViewSize.width / imgSize.width;
    CGFloat scaleH = imgViewSize.height / imgSize.height;
    CGFloat aspect=fmin(scaleW, scaleH);

    CGRect imageRect={ {0,0} , { imgSize.width*=aspect, imgSize.height*=aspect } };

    // Note: the above is the same as :
    // CGRect imageRect=CGRectMake(0,0,imgSize.width*=aspect,imgSize.height*=aspect) I just like this notation better

    // Center image

    imageRect.origin.x=(imgViewSize.width-imageRect.size.width)/2;
    imageRect.origin.y=(imgViewSize.height-imageRect.size.height)/2;

    // Add imageView offset

    imageRect.origin.x+=imgView.frame.origin.x;
    imageRect.origin.y+=imgView.frame.origin.y;

    return(imageRect);
}

For a better illustration of the differences between the three content modes, see below: