The broadcaster announced that Leeds is being considered as a possible home for its national headquarters or as a 'creative hub', along with Greater Manchester, Liverpool, West Midlands, Glasgow, Cardiff and and Bristol.
Sheffield is one of six bidders, along with Belfast, Brighton, Newcastle-Gateshead, Nottingham and Stoke-on-Trent, in the running only to host a creative hub.
A senior city councillor said it was "incredibly disappointing" not to have a chance to host the national HQ, but that being on the shortlist for a creative hub was "a catalyst for our next wave of transformation".
Hull, the 2017 UK City of Culture, was not among the 13 areas to make it through to the next stage of the process. The city council's deputy leader Darren Hale said: “We are disappointed to have missed out on reaching the next stage of Channel 4’s shortlisting process after putting together an ambitious bid but ultimately, you will never win the lottery if you never buy a ticket and like with the 2017 City of Culture, dreaming big and bold will lead to many successful and the odd near miss.
In total, 30 submissions were received from across the UK from authorities wanting to host the new national HQ and two creative hubs. The shortlist was put together by chief executive Alex Mahon and her team.
Each of the shortlisted cities will participate in a second stage process, which will include Channel 4 visiting each city for a presentation and Q&A.
After this, Channel 4 says it "will engage in further discussions with cities and regions as necessary" before selecting the final locations in October.
Under the relocation plan, a new national headquarters outside of London will be established along with two smaller creative hubs by 2019.
Overall, it will see 300 Channel 4 jobs being based in regions with 3,000 additional production jobs also being set up outside the capital.
Chief Commercial Officer, Jonathan Allan, who is leading the pitch process said: “We’ve been incredibly impressed both by the number of pitches we received and by the high quality of the submissions – which has underlined the huge amount of creativity, innovation and talent right across the UK.
“However we have to move to a shortlist phase and, after careful consideration by the Channel 4 Executive team, we’ve selected 13 cities that are best able to meet our vision for our new hubs in the Nations and Regions.
"We look forward to visiting all those on the shortlist as part of our second phase, but we will also be continuing to work with all cities and regions as part of our strategy to increase investment and support creative businesses, jobs and growth across the UK.”
Roger Marsh OBE, Chair of the Leeds City Region Enterprise Partnership, said : “Channel 4’s decision to include us on its shortlist is a significant achievement given some 30 areas put themselves forward to host the new national headquarters or one of the new creative hubs. It is also a signal of the strength of our submission.
“However while this is a positive step there is still a lot of hard work to do to secure the tremendous prize on offer and we will continue to work with our partners to achieve the outcome we all want to see and capitalise upon it.
“I believe firmly that what Channel 4 is looking for is also what we as a region desire; to harness our youth, celebrate our diversity, embrace our differences, nurture top talent and pioneer new technologies. Ultimately doing this will be the key to both of our successful futures.”
Sally Joynson, Chief Executive of Screen Yorkshire, which champions the region's film, TV, games and digital industries, said: “We are delighted that Channel 4 has shortlisted both Leeds City Region and Sheffield as potential hosts for its National HQ and Creative Hubs respectively.
"As Yorkshire locations on the east of the Pennines, we firmly believe they each have dynamic creative sectors that can both support Channel 4’s strategic plans and better reflect the rich diversity of voices the UK.
"We are looking forward to continuing our work with the Leeds City Region on the next stage of the selection process, where we can showcase the wealth of programme-making, digital expertise and talent that is located here.”
Thelma Walker, Labour MP for Colne Valley, said: “I am delighted that Channel 4 are considering Leeds to be their national headquarters.
"We have such a creative people in our region, and with the opportunities that Channel 4 relocating to Leeds would bring to the wider West Yorkshire Combined Authority area, it would help drive the Northern Powerhouse Project forward and be a huge boost to our local economy and employment.
"Colne Valley and wider Kirklees is already a creative hub and would massively benefit from Leeds being successful in their bid.”