在下列工具书中只有 under discussion，没有 on discussion。

1. 郭杰克主编《当代英语搭配大词典》(高等教育出版社 2002年11月第1版)P459:

Their case is under discussion.

2. 简清国主编《建宏 ۰外研社英汉多功能词典》(外语与教学研究出版社1997年1月第1版)P422: 

the question under discussion

3. 王文昌主编《英语搭配大词典》(江苏教育出版社1991年1月第1版)P495:

That’s another topic that will come under discussion.

Don’t deviate from the subject under discussion.

4. 张道真编著的《现代英语用法词典》(重排本) (外语教学与研究出版社1994年10月第1版)P348: 

be [come] under discussion

The question is still under discussion.

That has no relation to the matter under discussion.

That’s another topic that came under discussion.

5. 周国珍主编的《大学英语详注词典》（上海交通大学出版社 2002年9月第一版）P324:

under discussion

Their case is now under discussion.

6.《柯林斯COBUILD高阶英汉双解学习词典》(外语教学与研究出版社 2011年7月第1版)P737: 

If something is under discussion, it is still being talked about and a final decision has not yet been reached.

“The proposals are still under discussion,” she said.

7.《麦克米伦高阶英汉双解词典》 (杨信彰等译 外语教学与研究出版社 2005年10月第1版 ) P577: 

be underdiscussion(=being discussed)

Proposals for changing exsisting system are currently under discussion.

8. Longman Dictionary of Contemporary English(English ۰Chinese) (Fourth Edition) (光盘版): 

under discussion(=being discussed) the project is under discussion as a possible joint venture.

9.《牛津高阶英汉双解词典》(第7版) (商务印书馆 2009年 4月第3版) P569: 

The plans have been under discussion(=being talked about) for a year now.

10. (日) 市川繁治郎主编《英语搭配大辞典》(外语教学与研究出版社2006年10月第1版)P 523:

under discussion The bill, then under discussion in committee, seemed doomed to die before reaching the Senate floor.

另外，在英美国家的语料库中也极少有on discussion的真实例证。

①在BNC 上共有247例包含 under discussion 的例句，但仅有一例包含 on discussion 的例句：

I'm not seeking to close down on discussion about item three, one and three, three but in view of the discussion we took this morning,…

② 在COCA 共有403例包含 under discussion 的例句，但仅有一例包含 on discussion 的例句：

2005 Person centered planning activities had a positive effect on parent participation in IEP/TP meetings, but not on discussion of post-school issues during the meetings.

由此看来，under discussion 表示“在讨论中”是正确的表达形式；on discussion虽不能说绝对错误，但在英国英语和美国英语中几乎没有人使用。