On 29th August 2021 Norwich signed Norwegian international midfielder Mathias Normann on a season-long loan from Russian side FC Rostov. The Canaries have an option to make the deal for the 25-year-old permanent. He was the club's 10th recruitof the Summer 2021 transfer window.

Daniel Farke, Norwich's manager said "We're really happy to bring Mathias in. We've worked on this piece of business for several weeks. It's not easy for us to bring a player in who had many clubs interested in him. We see lots of potential in Mathias and he's capable to play in several roles. He's quite versatile in the midfield positions."

Normann played for the youthteam of his hometown Svolvaer before joining Lofoten in 2012. He moved to Bodo/Glimt in 2013, making his senior debut on 24th April 2014. During his time with Bodo/Glimt he was loaned to Alta.

He joined Brighton in 2017 but didn't make a first team appearance for the Seagulls and on 19th August 2017 he joined Molde on a loan that was extended to the summer of 2018. He made 18 appearances for Molde

On 28th January 2019, he signed with the Russian Premier League club FC Rostov and had made 56 appearances at the time of his loan to Norwich, scoring twice.

He made his international debut for Norway on 5th September 2019 against Malta in a Euro 2020 qualifier. His first international goal was against Serbia on 8th October 2020.

Normann made his Norwich debut on 18th September 2021 in a 3-1 home defeat to Watford in the Premier League. He scored his first goal for City in the 2-1 win at Brentford on 6th November 2021. He finished the season with 25 appearances and one goal as Norwich were relegated from the Premier League. He missed two months of the season with a pelvic injury.

Following the Russian invasion of Ukraine, Normann made it clear that he would not return to Rostov, despite being contracted until 2024. On 16th August 2022, Italian side Lecce, newly promoted to Serie A, announced that they had signed him on loan only for them to later report that the contract had been cancelled by mutual consent. Lecce expressed frustrations at the 'protracted nature relating to the registration' of Normann. A spokesperson for the ex-City man has moved to squash rumours that the cancellation of the deal was due to medical concerns around Normann but the decision was taken prior to the 26-year-old undergoing his medical at the Stadio Via del Mare. 

On 6th September 2022 it was reported that Normann was joining Dynamo Moscow on loan. Normann explained “It is quite simple. As of today, it is the best sporting opportunity I have. Then we ended up with that."

The Norwegian Football Federation released a statement on Monday, with quotes from president Lise Klaveness. It read: "National team manager Ståle Solbakken has this afternoon informed Mathias Normann that he is not relevant for the next national team meeting as he has stated that he is ready to sign for a new Russian club.  All of Norwegian and European football agree to put joint pressure on Russia as a belligerent party, which has also used positions of power in sport very actively. All Russian teams are banned from international sports competitions. Ståle and I agree that Normann cannot represent Norway when he will now play for a new Russian club.” 

Following Ukrainian drone attacks on Moscow, Normann cancelled his contract with FC Rostov and Dynamo Moscow, and moved to Saudi Arabia to join Al-Raed on 20th August 2023.