The 26-year-old Japanese winger joined on loan on transfer deadline day back in February in order to try to get more playing-time after struggling at Liverpool.
During his eight weeks at Southampton, he has already played more than in his five months of the campaign that he spent in Merseyside.
However, Ralph Hasenhuttl revealed whilst speaking to the media on Thursday that whilst Southampton have entered negotiations with Walcott over a permanent deal, they are not pursuing Minamino permanently.
"It is never nice for a player when you don't end up getting the game time that you want to have, when you only train and are not see as part of the first 11," he said whilst speaking with HampshireLive.
"This definitely then helps your mentality when you later get a lift and a chance to play. Players like to join big clubs because they get a lot of money there and they get a lot of praise for being a part of the top six, if you will."
"But it is only for a short moment that you are happy about it because when you are not playing enough times and you are not important for the club, then it feels very awful, very quickly."
"The most important thing for him is that he gets a chance to play. We had so much rotation with injuries and everything that it was clear he would get a lot of game time with us."
"At the moment, it is a little bit more difficult, I think, but we like his quality. He scored a few good goals for us so far. I am happy to have as an option."
Before concluding, he said "We haven't had any negotiations about Takumi so far. We are not aware of what Liverpool's plans are for him in the summer."
"The deal was simply to give him game time during the second half of the year. This is what we have done and, hopefully, he will get more chance to play for us."
Walcott's contract at Everton is set to expire at the end of the season, and the Toffees are not keen on extending his contract.
The 32-year-old has played in 17 Premier League games this season for Southampton, scoring two goals and providing three assists, and is proving to be a valuable member in Hasenhuttl's squad, playing either on the wings or as a secondary striker.