The broadcaster has confirmed it is establishing a new national HQ outside of London, which would house a creative hub and bring hundreds of jobs.
He highlighted the city’s already vibrant creative cluster as one of the UK's largest media production centres outside of London.
Cardiff will come up against tough competition from other UK cities such as Leeds, Bristol and Birmingham.
However, if the bid for the main HQ fails, Cardiff will bid for one of the two other creative hubs that the channel has committed to establishing.
Channel 4, which currently employs around 800 people, said it couldn't yet give a breakdown on job roles in each of the new operations, but it is thought that most would be located at the new HQ and creative hub.
Cardiff Council leader Huw Thomas said in his letter: “I have no hesitation in taking this opportunity to confirm to you our intention to bid to secure one of the new creative hubs.
“This is based on Cardiff’s widely acknowledged strengths as a nationally significant centre of broadcasting and cultural excellence.
“You will be aware that Cardiff is the centre of a booming creative industry sector, employing 15,000 people and worth around £1.06bn of GVA.
“The Bazalgette Review and Nesta’s latest creative nation report confirm our place as one of the UK’s largest media production centres outside of London with the BBC, S4C and ITV based in the city.
“I am aware that C4 already draws upon the expertise of a number of Cardiff’s independent businesses.
“The city’s skills base is second to none. Film, television, radio, video games, animation and post-production activities are at the heart of Cardiff’s creative growth, supported by world-class universities teaching over 7000 students in creative courses.”
“Channel 4 will no doubt wish to identify cities able to attract and retain talent and provide the right environment for relocating staff.
“Cardiff scores highly across these criteria. It is consistently recognised as one of the best places to live in by residents and in the latest EU Urban Audit Perception survey, Cardiff was voted the number one city in the UK for
“The Cardiff team look forward to meeting and presenting the Cardiff proposition to you shortly.
“Your proposal to invite cities to bid for these investments is an excellent idea and Cardiff would be delighted to present its credentials to you and your team.”
Channel 4 is expected to confirm the location of its new HQ and hubs in September.
Channel 4’s national and regional spending is also being significantly increased, from 35% to 50% of main channel UK commissions, by 2023 – which equates to more than £250m more in total.
Ms Mahon said: “As a public service broadcaster with diversity in its DNA, Channel 4 has a unique ability to reflect our society.
“This is a significant and exciting moment of change for Channel 4 as we evolve to ensure we are best suited to serve all of the UK.
“With this new strategy we will go even further to make sure that people right across the UK are represented on screen and in the make-up of our own organisation – and it will also build on what we already do to support creative businesses, jobs and economies in the nations and regions.”