Chairman Fawaz Al Hasawi has vowed to strengthen Nottingham Forest year on year, with loan arrivals possible.
A number of English clubs are tracking Helsingborgs hot-shot David Accam, Sky Sports understands.
The Royal Blues have appointed former under-17s coach Jens Keller in place of the sacked Huub Stevens until at least the end of the season.
Reports have linked Tuchel to the role next summer, but, with the two teams meeting in the DFB-Pokal on Tuesday night, the Mainz coach claimed he has had no contact with the Schalke bosses.
"I am under contract in Mainz until 2015 and I affirm that every day," he told reporters.
"There can be no doubt that my coaching team and I are getting the utmost joy and the utmost job satisfaction at this point.
"Up until now I have not spoken to any officials at Schalke."
Mainz general manager Christian Heidel claimed no amount of compensation could persuade the club to part with Tuchel, who took charge in 2009.
"Not for 30 or 60 million euros (will we let him go)," he said. "Even if a Russian comes in for him, or a Sheik."
Keller has admitted that even he never expected to be handed the top job at the Veltins Arena.
He told the club's website: "When I was unveiled as under-17 coach in the summer I never thought I'd take charge of the first team here.
"I was simply looking forward to an exciting challenge in the youth set-up. Working with the under-17s over the last few months has been great fun. The boys are eager to learn and have had a fantastic season so far.
"The biggest difference between youth football and professional football is that the game is even faster at this level. The intensity is almost the same, however. We trained under virtual professional conditions with the under-17s."
Keller's only previous Bundesliga coaching experience came in an ill-fated two-month spell in charge of Stuttgart early in the 2010/11 season.
On that occasion he stepped up from assistant coach and was thrown right into a hectic run of fixtures.
Keller reckons this time will be different because he will have time over the winter break to help put his stamp on the squad.
"Back then I was promoted from assistant coach to head coach and had eight games in the first four weeks," he said.
"Because of the busy fixture list it was virtually impossible to give the team new impetus. It's different this time because I'll have more time with the players after the cup game and I wasn't part of the senior coaching staff like I was in Stuttgart."
Schalke general manager Horst Heldt revealed the club decided not to make an external appointment because they had a ready-made replacement in Keller, whose under-17 side have a 100 per cent record this season.
Heldt said: "I know Jens from my time at Stuttgart (where Heldt was general manager) and am convinced he's an outstanding coach. He was a pro himself and has a wealth of experience. We hope he can deliver the impetus to get us back on track. We have every confidence in him.
"Why should we look further afield when we have good people here?"
On whether Keller will continue to lead the first team beyond the end of the season, Heldt added: "We'll wait and see how things develop and intend to manage the footballing side of things together for the time being.
"Our objective for the season remains automatic qualification for the group stage of next year's Champions League."