Enter your email below and we will contact you

My client wants a page in which the following text appears:

"Enter your email below and We will contact you"

It's then followed by a textfield (to write the email address) and a button to submit it.

Is this the right way ? Do people trust to enter their own emails to know more ? (actually immediately below the textfield reassures the user by saying: we don't share your email with anybody,...)

My question is: is an approach where we ask the user to enter their email any better than an approach where we ask to click on a e-mail us link ?