Darren Lewis of the Mirror reported the Potters attempt to jump ahead of the queue for the player's services, with David Wright of the Express declaring the Gunners are "rocked" by Stoke manager Mark Hughes' offer.
The former France under-21 international was a hit for Marseille during his two seasons at the Ligue 1 giants but moved to Porto last summer. He has struggled for form in Portugal, making him vulnerable to approaches in January.
Stoke have shown great ambition under Hughes' tenure, recruiting the likes of Xherdan Shaqiri and Bojan Krkic to form a dynamic core at the Britannia Stadium.
Wright explained Arsenal pursued Imbula in the summer before he opted to move to Porto, but coach Arsene Wenger has kept his eye on the player, remaining "keen to sign him."
Football writer Ben Jata lauded the player during Porto's 2-1 win against Chelsea in the Champions League:
Gianelli Imbula Wanga is nice! Wish I could watch him more often. #Porto— Ben Jata (@Ben_Jata) September 30, 2015
The 23-year-old has struggled to break into the first team at the Dragon Stadium, making only eight starts in the Primeira Liga since his £15 million switch, according to Wright.
Sky Sports quoted Hughes, when asked about the potential of capturing the midfielder, and the Stoke boss said:
It is inappropriate for me to talk about individual players, other than to say we're in the market for good players. We are actively looking. We think there are opportunities if everything falls into place, but there are a lot of factors.
We never get too ahead of ourselves because we know the potential pitfalls of the transfer process. We just have to be patient. If it happens, we'll be delighted. If we have to bide our time until the summer, so be it.
Here is a video showing why Wenger wanted to add Imbula to his squad:
In other news, Arsenal prodigy Alex Iwobi could temporarily leave the club, dropping down to the Championship on loan with Nottingham Forrest.
Local newspaper the Nottingham Post said the 19-year-old forward, who has made four appearances for the first team in the Premier League this term, could move to the east Midlands to play more first-team football.
Wenger praised the versatile player during pre-season, per the Nottingham Post. "I like his team attitude, his movement," said Wenger following Iwobi's goalscoring contribution in August's Emirate's Cup. "We have a game based on movement and speed, and he integrates that very well. He has good power and is usually efficient – he scores goals a lot."
Iwobi is one of Wenger's most promising youngsters, but he is ready to play football every week, and a spell at Forest will give him the opportunity.
Will Iwobi make it at Arsenal?
The teenager will be ready for increased game time in the Premier League next season and could find his way to a year-long loan to one of England's top-tier sides in 2016-17.
The potential loss of Imbula is unlikely to worry Wenger too much after he strengthened the midfield with Egyptian player Mohamed Elneny.
Elneny fits the squad needs down to a tee, bringing defensive energy to the centre of the park that Arsenal currently miss.