Southampton chairman Rupert Lowe visited Arsenal's training ground on Thursday as speculation grew that Theo Walcott could join the Gunners.
Lowe confirmed his visit to BBC Radio Solent but refused to comment further.
The Saints chairman had previously said on the club's radio station that he could not give any "copper-bottom" guarantees that Walcott will stay.
Walcott's agent Colin Gordon told BBC Sport: "Our only concern is Theo's best interest and development as a player."
"We want him to stay but I cannot give any copper-bottomed answers and say he will be here," said Lowe.
The striker has a pre-contract agreement with the Saints to sign a professional contract on his 17th birthday in March.
Lowe remains confident that Walcott will commit himself on 16 March, but admits he would be powerless if the youngster decided he wanted to take the plunge into the Premiership.
He added: "In the same way that supporters have jobs and sometimes move on, if he feels he is better served by a move then that is a matter for him.
"We hope that we are the right club to give him the right career path to progress. If he feels that then I'm sure he will stay.
"We want to get the best from him and for him to progress and flourish here, as he has done so far.
"But if at any stage he wants to go, then that will be a matter for him and his advisors and those he talks to."
Although all parties insist that money is not the main issue, BBC Sport understands the south-coast club are prepared to make Walcott the highest-paid teenager in the country.
Lowe said: "I'm not going into contractual details but the issue is he is still a scholar and signs as a pro at 17.
"All things being equal, that should happen. He is a young lad who will listen to his advisors and parents, and everything they say has got to be taken into account."
Walcott's representatives met Lowe, Saints director of football Sir Clive Woodward and academy director Huw Jennings earlier this week.
Saints' fear is that Walcott could break his pre-contract agreement and leave the club. Any compensation for his development would then be decided by a tribunal.
Charlton were awarded £1.2m by a tribunal when England star Jermain Defoe tore up his pre-contract agreement to join West Ham, who later sold him to Tottenham for £7m.
If Walcott signs a professional contract with Saints, it will give the south coast club scope to cash in on him later, with fees of up to £10m being discussed.