O'Neil, with a year remaining on his contract, is likely to be sold if an offer of around £4.5m is lodged for his services from a Premier League club before the transfer deadline on August 31.
It has been claimed in the last 24 hours that Stoke City have had a £2m offer rejected Strachan insists he knows only about talks for incoming deals for the Boro captain, who was also the subject of interest from Fulham and Blackburn earlier this year.
Stoke boss Tony Pulis, who handed the midfielder his first team debut at Portsmouth as a 16-year-old, would like to add O'Neil to his ranks before the start of the Premier League season.
But Strachan is in no rush to lose a player, one whose character in the dressing room he admires, after making progress on assembling the sort of squad he hopes can win the Championship next season.
O'Neil revealed he has had discussions with Strachan since returning to pre-season training and the 27-year-old is happy to stay.
I'm unaware of anything going on. I have heard the rumours and I have not heard anything from Middlesbrough, from any other club, any agent, that I will not be here next season, said O'Neil, a £5m signing by Gareth Southgate from Portsmouth three years ago.
I'm just focused on a tough Championship season, like we found out last season.
I have spoken to the gaffer, he is fine, I am fine.
He said he wanted me to stay and that he wanted me to give all I could for the club, like I always have, and I said that was fine by me and I will do everything I can for this club.
Hopefully we will have a more successful season than the last two because I have been here three years and the last two have been disappointing. Hopefully we can have something to celebrate at the end of this one.
There has been a much lighter and relaxed mood within the Middlesbrough camp in Ireland this week to that which travelled to Scotland for a pre-season break 12 months ago.
Following the disappointment of relegation from the Premier League, O'Neil was part of a squad which was waiting to be torn apart, with the likes of Robert Huth, Tuncay Sanli and Stewart Downing among those to moved on.
This year has been different, however.
Strachan has added five permanent signings to his squad and four of them the injured Andy Halliday apart have started both matches against Athlone Town and Bray Wanderers in Ireland.
The trip to Carton House in County Kildare has done some good, even if Middlesbrough face an anxious wait to learn the extent of the damage sustained to Kris Boyd's ankle at the Carlisle Grounds Stadium on Wednesday night.
Last year we knew we would lose five or six players, said O'Neil.
This year we knew we would gain five or six. It's a completely different atmosphere.
The gaffer is still trying to do a little bit of work. We could do with a bit of width and we have a lot of actual midfielders and not many wingers.
That makes us sometimes predictable in playing through the middle. We are progressing.
It's still early and we are only in our second game. It was a good exercise and there were a few positives to take. It will take a little while.
There's not been massive changes.
I don't think there are any players who have come in who do things out of the ordinary who can't fit in to the team we have played before.
The formation is the same.
It's important we make the most of the few games remaining before the season starts.
Source: Northern Echo
Source: Northern Echo